Level scheme of $^{153}$Sm obtained from $^{152}$Sm($n_{th}$,$\gamma$) reaction using $\gamma-\gamma$ coincidence spectrometer

TL;DR

This study maps the detailed gamma-ray decay scheme of $^{153}$Sm formed via neutron capture, revealing new cascades and levels, and providing insights into its nuclear structure through gamma coincidence measurements.

Contribution

The paper presents the first comprehensive level scheme of $^{153}$Sm from neutron capture, identifying new gamma transitions and levels, and assigning spins based on gamma cascade analysis.

Findings

Detected 576 gamma transitions from 386 cascades.

Identified 74 primary gamma transitions and 291 secondary transitions as new data.

Tentatively assigned spin 3/2 to 53 intermediate levels.

Abstract

The level scheme of the compound $^{153}$Sm nucleus formed via the $^{152}$Sm($n_{th}$,$\gamma$) reaction is studied by using the $\gamma-\gamma$ coincidence spectrometer at Dalat Nuclear Research Institute, Vietnam. All the gamma cascades, which correspond to the decays from the compound state to 12 final levels of 0 ($\frac{3}{2}^+$), 7.535 ($\frac{5}{2}^+$), 35.844 ($\frac{3}{2}^-$), 90.875 ($\frac{5}{2}^-$), 126.412 ($\frac{1}{2}^-$), 127.298 ($\frac{3}{2}^-$), 182.902 ($\frac{5}{2}^-$), 321.113 ($\frac{3}{2}^+$), 404.129 ($\frac{1}{2}^-$), 405.470 ($\frac{3}{2}^-$), 414.924 ($\frac{1}{2}^+$), and 481.088 ($\frac{3}{2}^+$) keV, have been measured. A total number of 386 cascades corresponding to 576 gamma transitions has been detected. Among these cascades, 103 primary gamma transitions together with their corresponding intermediate levels and 299 secondary transitions have been determined. In addition, 29 primary gamma transitions, 42 intermediate levels, and 8 secondary transitions have been found to be the same as those extracted from the ENSDF data. The remain 74 primary gamma transitions, 61 intermediate levels, and 291 secondary transitions are therefore considered as the new data. In particular, based on an assumption that most of the transitions are dipole, we have tentatively assigned the unique spin value of $\frac{3}{2}\hbar$ for 53 observed intermediate levels corresponding to the cascades from the compound state to the final ones of 7.535 ($\frac{5}{2}^+$), 90.875 ($\frac{5}{2}^-$), and 182.902 ($\frac{5}{2}^-$) keV, whereas the remain levels are assigned with the spin values in the range of $[\frac{1}{2},\frac{3}{2}]\hbar$...

Tables

Table 1. Table 1: Isotopic content of the target used in the present experiment.

Isotope	Percentage (%)	${\sigma }_{th}$ (barn) ncs
152Sm	98.7	206 $\pm$ 3
144Sm	0.01	1.64 $\pm$ 0.10
147Sm	0.06	57 $\pm$ 3
148Sm	0.07	2.4 $\pm$ 0.6
149Sm	0.13	40140 $\pm$ 600
150Sm	0.20	100 $\pm$ 4
154Sm	0.83	8.5 $\pm$ 0.5

Table 2. Table 2: Gamma-cascade transition energies and absolute intensities obtained from the 152 Sm( n t ​ h , γ subscript 𝑛 𝑡 ℎ 𝛾 n_{th},\gamma ) reaction. Primary transitions and intermediate levels corresponding to each gamma cascade are determined if possible. Comparisons between the data obtained within the present work with those extracted from the ENSDF library are made. Detailed explanation is given at the end of the table.

Present Work					ENSDF
$E_1$	$E_i$	$J_i$	$E_2$	$I_{\gamma \gamma }$	$E_f$	$E_1$a	$E_i$b	$J_i$
5238.0 3	630.4 7	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	630.4 3	5039 327	0 (${\frac{3}{2}}^{+}$)	5237.8 3	630.20 5f	${\frac{1}{2}}^{-},{\frac{3}{2}}^{-}$
			622.9 3	3695 316	7.535 (${\frac{5}{2}}^{+}$)
			594.6 4	462 98	35.844 (${\frac{3}{2}}^{-}$)
			539.5 3	487 95	90.875 (${\frac{5}{2}}^{-}$)
x5231.2 4			x629.7 4	485 114	7.535 (${\frac{5}{2}}^{+}$)
5172.7 4	695.7 8	$\frac{3}{2}$	696.0 4	312 77	0 (${\frac{3}{2}}^{+}$)	5172.7 3	695.80 4g	${\frac{1}{2}}^{-}$
			659.6 3	4562 321	35.844 (${\frac{3}{2}}^{-}$)
			604.8 5	175 54	90.875 (${\frac{5}{2}}^{-}$)
			568.2 3	1121 139	126.412 (${\frac{1}{2}}^{-}$)c
5133.2 3	735.2 7	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	735.2 3	553 104	0 (${\frac{3}{2}}^{+}$)	5133.3 8	734.873 23h	(${\frac{3}{2}}^{+},\frac{5}{2}$)
5118.3 4	750.1 8	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	750.4 5	267 70	0 (${\frac{3}{2}}^{+}$)	5117.8 5	750.32 5	${\left(\frac{3}{2}\right)}^{-}$
			714.1 3	805 133	35.844 (${\frac{3}{2}}^{-}$)
			659.3 3	1808 192	90.875 (${\frac{5}{2}}^{-}$)
			622.6 4	306 71	126.412 (${\frac{1}{2}}^{-}$)c
			567.2 3	693 130	182.902 (${\frac{5}{2}}^{-}$)
x5100.2 6			x768.2 6	124 51	0 (${\frac{3}{2}}^{+}$)
5079.9 5	788.5 9	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	788.9 5	250 68	0 (${\frac{3}{2}}^{+}$)	5078.86	788.92 5	${\frac{3}{2}}^{+}$
			780.5 6	186 63	7.535 (${\frac{5}{2}}^{+}$)
4951.5 3	916.9 7	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	881.1 3	654 119	35.844 (${\frac{3}{2}}^{-}$)	4951.5 6	917.1 5	(${\frac{3}{2}}^{+}$)
			826.0 3	324 77	90.875 (${\frac{5}{2}}^{-}$)
4884.6 5	983.8 9	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	984.3 3	1576 130	0 (${\frac{3}{2}}^{+}$)	4884.0 8	984.2 4i	${\frac{3}{2}}^{+}$
			976.8 3	1302 151	7.535 (${\frac{5}{2}}^{+}$)
			947.2 6	154 49	35.844 (${\frac{3}{2}}^{-}$)
			801.6 5	143 47	182.902 (${\frac{5}{2}}^{-}$)
			662.0 5	169 60	321.113 (${\frac{3}{2}}^{+}$)
			568.6 7	234 96	414.924 (${\frac{1}{2}}^{+}$)
x4810.1 5			x737.2 5	109 43	321.113 (${\frac{3}{2}}^{+}$)
x4806.1 8			x581.2 8	194 92	481.088 (${\frac{3}{2}}^{+}$)
x4794.2 6			x659.3 6	159 76	414.924 (${\frac{1}{2}}^{+}$)
4769.6 4	1098.8 8	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1098.8 4	216 50	0 (${\frac{3}{2}}^{+}$)	4770.57	1097.8 5	${\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$
4757.4 6	1111.0 10	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1074.5 5	202 57	35.844 (${\frac{3}{2}}^{-}$)	4757.9 7	1109.7 4	${\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$
			1020.6 6	98 39	90.875 (${\frac{5}{2}}^{-}$)
			984.5 5	97 37	126.412 (${\frac{1}{2}}^{-}$)c
			927.3 6	97 36	182.902 (${\frac{5}{2}}^{-}$)
x4724.2 4			x738.7 4	128 40	404.129 (${\frac{1}{2}}^{-}$)d
x4719.4 7			x827.9 7	45 23	321.113 (${\frac{3}{2}}^{+}$)
x4711.0 8			x1030.1 8	70 30	126.412 (${\frac{1}{2}}^{-}$)c
4704.8 6	1163.6 10	$\frac{1}{2},\frac{3}{2}$	1163.5 5	144 45	0 (${\frac{3}{2}}^{+}$)
			1036.4 7	66 30	126.412 (${\frac{1}{2}}^{-}$)c
4697.4 4	1171.0 8	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1171.3 4	190 58	0 (${\frac{3}{2}}^{+}$)	4697.2 7	1171.1 3	${\frac{1}{2}}^{-},{\frac{3}{2}}^{-}$
			1163.0 3	1132 167	7.535 (${\frac{5}{2}}^{+}$)
			1134.5 4	377 81	35.844 (${\frac{3}{2}}^{-}$)
			1079.9 3	843 111	90.875 (${\frac{5}{2}}^{-}$)
			1044.2 4	345 72	126.412 (${\frac{1}{2}}^{-}$)c
			988.3 3	537 89	182.902 (${\frac{5}{2}}^{-}$)
			849.4 3	701 112	321.113 (${\frac{3}{2}}^{+}$)
			766.1 4	430 88	404.129 (${\frac{1}{2}}^{-}$)d
			755.4 4	701 172	414.924 (${\frac{1}{2}}^{+}$)
			691.0 8	188 89	481.088 (${\frac{3}{2}}^{+}$)
x4676.6 9			x870.7 9	51 24	321.113 (${\frac{3}{2}}^{+}$)
x4674.2 6			x713.1 6	117 56	481.088 (${\frac{3}{2}}^{+}$)
4645.1 4	1223.3 8	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1223.2 5	191 54	0 (${\frac{3}{2}}^{+}$)	4644.6 10	1224.3 4	${\left(\frac{3}{2}\right)}^{+}$
			902.0 3	505 94	321.113 (${\frac{3}{2}}^{+}$)
4546.2 5	1322.2 9	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1195.3 6	64 28	126.412 (${\frac{1}{2}}^{-}$)c	4545.7 4	1322.1 3	${\frac{1}{2}}^{-},{\frac{3}{2}}^{-}$
			1000.7 5	167 52	321.113 (${\frac{3}{2}}^{+}$)
			917.2 6	170 57	404.129 (${\frac{1}{2}}^{-}$)d
			906.9 3	2174 315	414.924 (${\frac{1}{2}}^{+}$)
			840.8 3	4053 379	481.088 (${\frac{3}{2}}^{+}$)
4525.4 4	1343.0 8	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1215.9 3	1058 121	126.412 (${\frac{1}{2}}^{-}$)c	4525.29	1344.0 6	${\left(\frac{3}{2}\right)}^{+}$
			1160.2 3	761 110	182.902 (${\frac{5}{2}}^{-}$)
			937.3 4	75 22	404.129 (${\frac{1}{2}}^{-}$)d
x4518.0 5			x945.0 5	63 24	404.129 (${\frac{1}{2}}^{-}$)d
4507.4 4	1361.0 8	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	945.9 3	1712 220	414.924 (${\frac{1}{2}}^{+}$)	4507.41	1360.9 5	${\frac{1}{2}}^{-},{\frac{3}{2}}^{-}$
			880.3 5	384 111	481.088 (${\frac{3}{2}}^{+}$)
4503.2 4	1365.2 8	$\frac{3}{2}$	1274.1 6	180 52	90.875 (${\frac{5}{2}}^{-}$)
			960.1 3	368 64	404.129 (${\frac{1}{2}}^{-}$)d
4475.7 7	1392.7 11	$\frac{1}{2},\frac{3}{2}$	987.5 5	90 29	404.129 (${\frac{1}{2}}^{-}$)d	4474.4 8	1393.9 8f
			977.4 9	87 49	414.924 (${\frac{1}{2}}^{+}$)
4471.4 6	1397.0 10	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	982.3 8	118 57	414.924 (${\frac{1}{2}}^{+}$)	4472.76	1395.6 6	${\frac{3}{2}}^{+},{\frac{5}{2}}^{+}$
			915.7 5	371 107	481.088 (${\frac{3}{2}}^{+}$)
4467.6 4	1400.8 8	$\frac{1}{2},\frac{3}{2}$	1400.5 4	220 62	0 (${\frac{3}{2}}^{+}$)	4468.3 8	1400.0 8	(${\frac{5}{2}}^{-}$)
			995.7 3	296 58	404.129 (${\frac{1}{2}}^{-}$)d
x4456.3 5			x1412.1 5	141 49	0 (${\frac{3}{2}}^{+}$)
4445.6 4	1422.8 8	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1414.6 4	314 76	7.535 (${\frac{5}{2}}^{+}$)	4446.81	1421.5 7	${\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$
			1018.1 4	132 37	404.129 (${\frac{1}{2}}^{-}$)d
4432.6 5	1435.8 9	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1436.1 4	385 82	0 (${\frac{3}{2}}^{+}$)	4432.97	1435.4 3	${\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$
			1114.5 7	90 40	321.113 (${\frac{3}{2}}^{+}$)
			954.8 4	366 104	481.088 (${\frac{3}{2}}^{+}$)
x4424.4 6			x1038.6 6	69 29	404.129 (${\frac{1}{2}}^{-}$)d
x4422.7 9			x964.6 9	152 65	481.088 (${\frac{3}{2}}^{+}$)
4420.1 7	1448.3 11	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1033.4 7	160 61	414.924 (${\frac{1}{2}}^{+}$)	4420.73	1447.6 4	($\frac{3}{2}){}^{-}$
x4417.8 4			x1414.8 4	284 67	35.844 (${\frac{3}{2}}^{-}$)
x4401.0 7			x1340.1 7	85 32	126.412 (${\frac{1}{2}}^{-}$)c
4382.1 5	1486.3 9	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1486.8 4	398 93	0 (${\frac{3}{2}}^{+}$)	4382.60	1485.7 4	(${\frac{3}{2}}^{+}$)
			1450.7 6	144 46	35.844 (${\frac{3}{2}}^{-}$)
			1359.3 6	77 33	126.412 (${\frac{1}{2}}^{-}$)c
			1303.0 6	168 51	182.902 (${\frac{5}{2}}^{-}$)
			1164.4 4	344 83	321.113 (${\frac{3}{2}}^{+}$)
			1071.5 8	78 39	414.924 (${\frac{1}{2}}^{+}$)
x4376.9 8			x1170.4 8	66 32	321.113 (${\frac{3}{2}}^{+}$)
4354.7 5	1513.7 9	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1506.2 4	355 81	7.535 (${\frac{5}{2}}^{+}$)	4355.51	1512.8 3	(${\frac{3}{2}}^{+}$)
			1477.7 5	186 53	35.844 (${\frac{3}{2}}^{-}$)
			1423.0 3	534 96	90.875 (${\frac{5}{2}}^{-}$)
			1193.1 6	114 43	321.113 (${\frac{3}{2}}^{+}$)
			1098.3 5	201 68	414.924 (${\frac{1}{2}}^{+}$)
4340.9 4	1527.5 8	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1491.6 3	491 88	35.844 (${\frac{3}{2}}^{-}$)	4341.4 15	1527.0 5	(${\frac{1}{2}}^{-},{\frac{3}{2}}^{-}$)
			1400.2 3	688 93	126.412 (${\frac{1}{2}}^{-}$)c
			1206.1 5	149 50	321.113 (${\frac{3}{2}}^{+}$)
			1122.3 4	215 58	404.129 (${\frac{1}{2}}^{-}$)d
			1046.3 3	2820 296	481.088 (${\frac{3}{2}}^{+}$)
4329.1 3	1539.3 7	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1448.4 3	348 79	90.875 (${\frac{5}{2}}^{-}$)	4330.24	1538.1 5	${\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$
4311.0 4	1557.4 8	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1521.6 4	234 59	35.844 (${\frac{3}{2}}^{-}$)	4310.6 15	1557.7 15	${\frac{1}{2}}^{+},{\frac{3}{2}}^{+}$
			1430.5 5	112 37	126.412 (${\frac{1}{2}}^{-}$)c
			1236.2 3	540 103	321.113 (${\frac{3}{2}}^{+}$)
			1076.2 3	1267 196	481.088 (${\frac{3}{2}}^{+}$)
4242.1 4	1626.3 8	$\frac{1}{2},\frac{3}{2}$	1626.7 5	326 73	0 (${\frac{3}{2}}^{+}$)
			1220.4 3	551 93	404.129 (${\frac{1}{2}}^{-}$)d
x4240.1 6			x1307.2 6	98 39	321.113 (${\frac{3}{2}}^{+}$)
x4233.8 8			x1229.1 8	92 38	404.129 (${\frac{1}{2}}^{-}$)d
4207.8 6	1660.6 10	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1624.9 6	163 51	35.844 (${\frac{3}{2}}^{-}$)		1662	($\frac{3}{2}){}^{+}$
			1477.6 6	83 34	182.902 (${\frac{5}{2}}^{-}$)
x4191.8 4			x1585.8 4	184 51	90.875 (${\frac{5}{2}}^{-}$)
x4143.3 6			x1597.8 6	76 31	126.412 (${\frac{1}{2}}^{-}$)c
4128.7 5	1739.7 9	$\frac{3}{2}$	1740.3 3	324 75	0 (${\frac{3}{2}}^{+}$)
			1648.5 6	131 45	90.875 (${\frac{5}{2}}^{-}$)
			1612.2 5	162 47	126.412 (${\frac{1}{2}}^{-}$)c
			1556.5 3	411 81	182.902 (${\frac{5}{2}}^{-}$)
			1418.0 8	116 50	321.113 (${\frac{3}{2}}^{+}$)
			1333.8 3	280 62	404.129 (${\frac{1}{2}}^{-}$)d
			1258.9 8	87 45	481.088 (${\frac{3}{2}}^{+}$)
4115.9 5	1752.5 9	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1752.7 3	1377 157	0 (${\frac{3}{2}}^{+}$)		1751.4 5	$\frac{1}{2},\frac{3}{2}$
			1745.3 3	1044 146	7.535 (${\frac{5}{2}}^{+}$)
			1624.1 6	92 33	126.412 (${\frac{1}{2}}^{-}$)c
			1431.9 8	138 55	321.113 (${\frac{3}{2}}^{+}$)
x4114.1 5			x1273.2 5	136 53	481.088 (${\frac{3}{2}}^{+}$)
4099.8 5	1768.6 9	$\frac{1}{2},\frac{3}{2}$	1768.2 5	238 71	0 (${\frac{3}{2}}^{+}$)
			1732.7 5	181 57	35.844 (${\frac{3}{2}}^{-}$)
			1363.7 3	408 75	404.129 (${\frac{1}{2}}^{-}$)d
x4095.3 8			x1773.1 8	136 56	0 (${\frac{3}{2}}^{+}$)
4078.4 5	1790.0 9	$\frac{3}{2}$	1789.7 4	257 67	0 (${\frac{3}{2}}^{+}$)
			1607.0 6	104 39	182.902 (${\frac{5}{2}}^{-}$)
			1384.8 4	236 56	404.129 (${\frac{1}{2}}^{-}$)d
x4074.8 8			x1472.5 8	84 40	321.113 (${\frac{3}{2}}^{+}$)
4035.1 5	1833.3 9	$\frac{3}{2}$	1797.0 5	172 56	35.844 (${\frac{3}{2}}^{-}$)		1833	($\frac{5}{2}){}^{+}$
			1743.2 6	153 53	90.875 (${\frac{5}{2}}^{-}$)
			1427.4 3	418 75	404.129 (${\frac{1}{2}}^{-}$)d
4027.0 5	1841.4 9	$\frac{3}{2}$	1805.5 4	259 68	35.844 (${\frac{3}{2}}^{-}$)		1840	${\left(\frac{5}{2}\right)}^{+}$
			1750.6 5	212 58	90.875 (${\frac{5}{2}}^{-}$)
x4024.3 7			x1661.2 7	141 47	182.902 (${\frac{5}{2}}^{-}$)
x4019.5 5			x1721.6 5	103 36	126.412 (${\frac{1}{2}}^{-}$)c
3992.2 5	1876.2 9	$\frac{3}{2}$	1785.1 6	152 48	90.875 (${\frac{5}{2}}^{-}$)
			1471.0 5	112 37	404.129 (${\frac{1}{2}}^{-}$)d
3983.0 5	1885.4 9	$\frac{1}{2},\frac{3}{2}$	1758.1 3	336 61	126.412 (${\frac{1}{2}}^{-}$)c		1884	(${\frac{5}{2}}^{-},{\frac{7}{2}}^{-}$)
			1480.0 6	143 43	404.129 (${\frac{1}{2}}^{-}$)d
x3981.2 6			x1796.3 6	133 45	90.875 (${\frac{5}{2}}^{-}$)
x3970.8 4			x1492.2 4	186 50	404.129 (${\frac{1}{2}}^{-}$)d
x3956.3 4			x1506.7 4	146 42	404.129 (${\frac{1}{2}}^{-}$)d
x3945.4 6			x1601.8 6	100 40	321.113 (${\frac{3}{2}}^{+}$)
3942.6 5	1925.8 9	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1798.3 6	129 38	126.412 (${\frac{1}{2}}^{-}$)c	3943.5 8	1924.9 8	${\frac{3}{2}}^{+},{\frac{5}{2}}^{+}$
			1520.7 5	139 44	404.129 (${\frac{1}{2}}^{-}$)d
3934.9 5	1933.5 9	$\frac{1}{2},\frac{3}{2}$	1897.6 3	705 111	35.844 (${\frac{3}{2}}^{-}$)	3934.6 6	1933.8	($\frac{5}{2}){}^{+}$
			1806.8 4	164 42	126.412 (${\frac{1}{2}}^{-}$)c
			1613.4 6	200 63	321.113 (${\frac{3}{2}}^{+}$)
			1451.5 4	300 90	481.088 (${\frac{3}{2}}^{+}$)
3932.3 5	1936.1 9	$\frac{3}{2}$	1936.5 4	415 91	0 (${\frac{3}{2}}^{+}$)
			1929.4 5	317 80	7.535 (${\frac{5}{2}}^{+}$)
			1844.9 5	183 55	90.875 (${\frac{5}{2}}^{-}$)
			1752.2 5	105 41	182.902 (${\frac{5}{2}}^{-}$)
x3900.7 3			x1840.4 3	530 76	126.412 (${\frac{1}{2}}^{-}$)c
x3887.8 6			x1659.5 6	145 51	321.113 (${\frac{3}{2}}^{+}$)
x3885.2 4			x1800.3 4	219 62	182.902 (${\frac{5}{2}}^{-}$)
3830.9 5	2037.5 9	$\frac{1}{2},\frac{3}{2}$	2037.3 5	218 65	0 (${\frac{3}{2}}^{+}$)
			2001.7 4	305 72	35.844 (${\frac{3}{2}}^{-}$)
			1910.3 6	183 54	126.412 (${\frac{1}{2}}^{-}$)c
			1556.7 5	229 81	481.088 (${\frac{3}{2}}^{+}$)
x3829.3 6			x1948.3 6	155 54	90.875 (${\frac{5}{2}}^{-}$)
x3781.5 6			x2086.9 6	226 77	0 (${\frac{3}{2}}^{+}$)
3777.4 5	2091.0 9	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	2055.2 5	226 62	35.844 (${\frac{3}{2}}^{-}$)		2092	($\frac{3}{2}){}^{+}$
			1685.5 3	483 91	404.129 (${\frac{1}{2}}^{-}$)d
			1610.0 7	222 82	481.088 (${\frac{3}{2}}^{+}$)
3757.3 4	2111.1 8	$\frac{3}{2}$	2075.2 4	406 86	35.844 (${\frac{3}{2}}^{-}$)
			2020.4 3	572 108	90.875 (${\frac{5}{2}}^{-}$)
x3754.5 7			x1931.0 7	101 45	182.902 (${\frac{5}{2}}^{-}$)
x3752.1 10			x2080.5 10	127 51	35.844 (${\frac{3}{2}}^{-}$)
x3736.4 8			x1949.0 8	94 42	182.902 (${\frac{5}{2}}^{-}$)
3733.0 6	2135.4 10	$\frac{1}{2},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	1814.0 6	189 64	321.113 (${\frac{3}{2}}^{+}$)		2135	${\frac{3}{2}}^{+},{\frac{5}{2}}^{+}$
			1730.3 6	138 54	404.129 (${\frac{1}{2}}^{-}$)d
3709.8 6	2158.6 10	$\frac{3}{2}$	2122.6 5	299 77	35.844 (${\frac{3}{2}}^{-}$)		e2167 13
			1974.9 7	122 54	182.902 (${\frac{5}{2}}^{-}$)
			1754.1 6	174 56	404.129 (${\frac{1}{2}}^{-}$)d
3693.6 6	2174.8 10	$\frac{1}{2},\frac{3}{2}$	2174.5 5	369 97	0 (${\frac{3}{2}}^{+}$)		e2167 13
			2139.4 7	169 59	35.844 (${\frac{3}{2}}^{-}$)
			1769.3 5	156 54	404.129 (${\frac{1}{2}}^{-}$)d
3676.1 5	2192.3 9	$\frac{1}{2},\frac{3}{2}$	2156.2 4	276 74	35.844 (${\frac{3}{2}}^{-}$)		e2188 15
			2065.1 4	261 62	126.412 (${\frac{1}{2}}^{-}$)c
			1711.5 7	157 75	481.088 (${\frac{3}{2}}^{+}$)
x3655.6 6			x1807.3 6	164 56	404.129 (${\frac{1}{2}}^{-}$)d
3644.6 6	2223.8 10	$\frac{1}{2},\frac{3}{2}$	2097.0 5	223 80	126.412 (${\frac{1}{2}}^{-}$)c
			1817.8 7	161 55	404.129 (${\frac{1}{2}}^{-}$)d
3630.7 7	2237.7 11	$\frac{3}{2}$	2229.3 4	186 58	7.535 (${\frac{5}{2}}^{+}$)		2239 12
			2054.9 7	152 56	182.902 (${\frac{5}{2}}^{-}$)
			1917.3 7	127 53	321.113 (${\frac{3}{2}}^{+}$)
x3611.2 7			x1936.1 7	91 43	321.113 (${\frac{3}{2}}^{+}$)
x3607.8 6			x1779.5 6	177 77	481.088 (${\frac{3}{2}}^{+}$)
x3582.2 5			x2103.3 5	236 69	182.902 (${\frac{5}{2}}^{-}$)
3574.8 6	2293.6 10	$\frac{1}{2},\frac{3}{2}$	1972.0 6	177 68	321.113 (${\frac{3}{2}}^{+}$)		e2286 11
			1888.7 6	160 56	404.129 (${\frac{1}{2}}^{-}$)d
x3569.2 8			x2171.9 8	164 63	126.412 (${\frac{1}{2}}^{-}$)c
x3544.3 5			x2288.3 5	212 62	35.844 (${\frac{3}{2}}^{-}$)
x3539.9 7			x2145.6 7	154 59	182.902 (${\frac{5}{2}}^{-}$)
3533.5 6	2334.9 10	$\frac{3}{2}$	2334.8 4	440 112	0 (${\frac{3}{2}}^{+}$)		e2332 15
			2152.1 7	119 49	182.902 (${\frac{5}{2}}^{-}$)
3526.2 5	2342.2 9	$\frac{3}{2}$	2305.5 5	225 66	35.844 (${\frac{3}{2}}^{-}$)		e2332 15
			2250.8 4	262 83	90.875 (${\frac{5}{2}}^{-}$)
			2215.7 4	510 114	126.412 (${\frac{1}{2}}^{-}$)c
			2159.6 4	417 96	182.902 (${\frac{5}{2}}^{-}$)
			2021.3 7	178 61	321.113 (${\frac{3}{2}}^{+}$)
x3506.4 7			x2234.7 7	235 78	126.412 (${\frac{1}{2}}^{-}$)c
x3482.0 6			x2203.5 6	231 70	182.902 (${\frac{5}{2}}^{-}$)
x3479.9 6			x2067.4 6	128 50	321.113 (${\frac{3}{2}}^{+}$)
x3475.5 5			x1987.5 5	251 70	404.129 (${\frac{1}{2}}^{-}$)d
3453.1 6	2415.3 10	$\frac{1}{2},\frac{3}{2}$	2094.2 6	153 57	321.113 (${\frac{3}{2}}^{+}$)		e2413 15
			2009.7 6	209 64	404.129 (${\frac{1}{2}}^{-}$)d
3448.9 5	2419.5 9	$\frac{3}{2}$	2412.5 5	339 84	7.535 (${\frac{5}{2}}^{+}$)		e2413 15
			2328.0 5	196 75	90.875 (${\frac{5}{2}}^{-}$)
3440.5 7	2427.9 11	$\frac{3}{2}$	2336.4 9	114 51	90.875 (${\frac{5}{2}}^{-}$)		e2413 15
			2023.0 6	233 68	404.129 (${\frac{1}{2}}^{-}$)d
3420.8 6	2447.6 10	$\frac{1}{2},\frac{3}{2}$	2319.9 4	267 60	126.412 (${\frac{1}{2}}^{-}$)c		e2456 11
			1967.0 8	186 81	481.088 (${\frac{3}{2}}^{+}$)
3407.3 4	2461.1 8	$\frac{3}{2}$	2278.1 4	357 89	182.902 (${\frac{5}{2}}^{-}$)		e2456 11
			1980.1 5	294 100	481.088 (${\frac{3}{2}}^{+}$)
x3396.8 5			x2344.3 5	131 43	126.412 (${\frac{1}{2}}^{-}$)c
x3388.9 7			x2158.4 7	92 46	321.113 (${\frac{3}{2}}^{+}$)
3384.7 7	2483.7 11	$\frac{1}{2},\frac{3}{2}$	2356.4 6	121 40	126.412 (${\frac{1}{2}}^{-}$)c		2484 11
			2078.3 6	191 63	404.129 (${\frac{1}{2}}^{-}$)d
			2002.6 8	240 96	481.088 (${\frac{3}{2}}^{+}$)
3373.7 6	2494.7 10	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	2487.9 5	339 83	7.535 (${\frac{5}{2}}^{+}$)		2496.6 12j	$\frac{1}{2},\frac{3}{2},\frac{5}{2}$
			2458.7 6	263 73	35.844 (${\frac{3}{2}}^{-}$)
3371.3 5	2497.1 9	$\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	2497.8 5	404 102	0 (${\frac{3}{2}}^{+}$)	3371.8 12	2496.6 12j	$\frac{1}{2},\frac{3}{2},\frac{5}{2}$
			2405.8 7	288 85	90.875 (${\frac{5}{2}}^{-}$)
			2369.7 5	234 56	126.412 (${\frac{1}{2}}^{-}$)c
			2313.8 5	311 83	182.902 (${\frac{5}{2}}^{-}$)
			2176.4 5	370 96	321.113 (${\frac{3}{2}}^{+}$)
x3366.4 7			x2411.2 7	160 63	90.875 (${\frac{5}{2}}^{-}$)
3355.2 5	2513.2 9	$\frac{3}{2}$	2477.7 3	520 87	35.844 (${\frac{3}{2}}^{-}$)		e2506 14
			2329.9 6	152 53	182.902 (${\frac{5}{2}}^{-}$)
x3338.2 6			x2402.9 6	117 39	126.412 (${\frac{1}{2}}^{-}$)c
3325.8 5	2542.6 9	$\frac{3}{2}$	2535.0 7	142 54	7.535 (${\frac{5}{2}}^{+}$)		e2534 11
			2506.6 5	196 54	35.844 (${\frac{3}{2}}^{-}$)
			2451.2 6	277 87	90.875 (${\frac{5}{2}}^{-}$)
			2222.2 4	164 61	321.113 (${\frac{3}{2}}^{+}$)
3322.9 6	2545.5 10	$\frac{3}{2}$	2418.0 5	237 56	126.412 (${\frac{1}{2}}^{-}$)c
			2363.7 5	298 77	182.902 (${\frac{5}{2}}^{-}$)
x3318.5 5			x2542.4 5	238 66	7.535 (${\frac{5}{2}}^{+}$)
x3272.3 7			x2275.0 7	127 45	321.113 (${\frac{3}{2}}^{+}$)
x3264.1 7			x2283.2 7	77 37	321.113 (${\frac{3}{2}}^{+}$)
x3261.0 4			x2607.4 4	607 119	0 (${\frac{3}{2}}^{+}$)
x3259.1 6			x2573.5 6	189 55	35.844 (${\frac{3}{2}}^{-}$)
x3252.5 4			x2294.8 4	120 39	321.113 (${\frac{3}{2}}^{+}$)
x3250.6 7			x2212.4 7	167 59	404.129 (${\frac{1}{2}}^{-}$)d
x3230.8 4			x2601.8 4	286 65	35.844 (${\frac{3}{2}}^{-}$)
3224.9 5	2643.5 9	$\frac{\mathrm{𝟏}}{\mathrm{𝟐}},\frac{\mathrm{𝟑}}{\mathrm{𝟐}}$	2643.6 5	302 84	0 (${\frac{3}{2}}^{+}$)	3225.6 7	2642.8 7	$\frac{1}{2},\frac{3}{2},\frac{5}{2}$
			2322.3 4	227 63	321.113 (${\frac{3}{2}}^{+}$)
x3223.2 8			x2239.7 8	119 56	404.129 (${\frac{1}{2}}^{-}$)d
3196.2 5	2672.2 9	$\frac{3}{2}$	2672.3 6	285 94	0 (${\frac{3}{2}}^{+}$)		e2669 15
			2664.2 5	242 70	7.535 (${\frac{5}{2}}^{+}$)
			2636.4 3	482 84	35.844 (${\frac{3}{2}}^{-}$)
			2545.2 6	177 54	126.412 (${\frac{1}{2}}^{-}$)c
			2266.8 5	271 79	404.129 (${\frac{1}{2}}^{-}$)d
3190.6 7	2677.8 11	$\frac{1}{2},\frac{3}{2}$	2677.7 6	391 107	0 (${\frac{3}{2}}^{+}$)		e2669 15
			2272.4 9	121 59	404.129 (${\frac{1}{2}}^{-}$)d
3187.3 3	2681.1 7	$\frac{3}{2}$	2645.5 3	508 87	35.844 (${\frac{3}{2}}^{-}$)		e2686 11
			2589.9 4	455 108	90.875 (${\frac{5}{2}}^{-}$)
3176.8 5	2691.6 9	$\frac{3}{2}$	2684.1 5	346 83	7.535 (${\frac{5}{2}}^{+}$)		e2686 11
			2654.8 6	176 57	35.844 (${\frac{3}{2}}^{-}$)
			2599.6 6	261 91	90.875 (${\frac{5}{2}}^{-}$)
			2565.5 5	314 78	126.412 (${\frac{1}{2}}^{-}$)c
			2509.1 3	463 91	182.902 (${\frac{5}{2}}^{-}$)
			2286.6 5	236 73	404.129 (${\frac{1}{2}}^{-}$)d
x3169.9 7			x2293.0 7	197 66	404.129 (${\frac{1}{2}}^{-}$)d
3168.7 4	2699.7 8	$\frac{3}{2}$	2692.4 4	367 86	7.535 (${\frac{5}{2}}^{+}$)
			2572.8 3	623 103	126.412 (${\frac{1}{2}}^{-}$)c
			2516.7 3	662 111	182.902 (${\frac{5}{2}}^{-}$)
			2378.1 7	149 53	321.113 (${\frac{3}{2}}^{+}$)
3158.3 5	2710.1 9	$\frac{3}{2}$	2619.3 7	185 70	90.875 (${\frac{5}{2}}^{-}$)		e2721 12
			2582.6 4	397 92	126.412 (${\frac{1}{2}}^{-}$)c
3153.7 5	2714.7 9	$\frac{1}{2},\frac{3}{2}$	2679.3 5	210 63	35.844 (${\frac{3}{2}}^{-}$)		e2721 12
			2392.9 5	220 67	321.113 (${\frac{3}{2}}^{+}$)
			2309.4 4	244 64	404.129 (${\frac{1}{2}}^{-}$)d
3145.5 5	2722.9 9	$\frac{3}{2}$	2722.4 5	472 117	0 (${\frac{3}{2}}^{+}$)		e2721 12
			2714.8 5	344 84	7.535 (${\frac{5}{2}}^{+}$)
			2632.6 6	208 74	90.875 (${\frac{5}{2}}^{-}$)
			2596.2 6	177 55	126.412 (${\frac{1}{2}}^{-}$)c
x3125.9 5			x2421.4 5	315 82	321.113 (${\frac{3}{2}}^{+}$)
x3124.4 4			x2708.2 4	390 82	35.844 (${\frac{3}{2}}^{-}$)
x3121.3 5			x2341.6 5	266 67	404.129 (${\frac{1}{2}}^{-}$)d
3111.5 4	2756.9 8	$\frac{1}{2},\frac{3}{2}$	2629.1 5	285 71	126.412 (${\frac{1}{2}}^{-}$)c		e2751 12
			2351.9 3	415 88	404.129 (${\frac{1}{2}}^{-}$)d
x3091.3 6			x2371.6 6	168 54	404.129 (${\frac{1}{2}}^{-}$)d
x3086.0 6			x2782.4 6	316 108	0 (${\frac{3}{2}}^{+}$)
x3082.8 9			x2464.5 9	121 67	321.113 (${\frac{3}{2}}^{+}$)
3079.5 5	2788.9 9	$\frac{3}{2}$	2789.3 5	540 133	0 (${\frac{3}{2}}^{+}$)		2788 14
			2780.7 4	418 90	7.535 (${\frac{5}{2}}^{+}$)
			2752.9 4	443 88	35.844 (${\frac{3}{2}}^{-}$)
			2699.0 6	257 81	90.875 (${\frac{5}{2}}^{-}$)
			2661.8 5	296 72	126.412 (${\frac{1}{2}}^{-}$)c
			2605.0 5	226 62	182.902 (${\frac{5}{2}}^{-}$)
x3067.2 6			x2618.3 6	108 44	182.902 (${\frac{5}{2}}^{-}$)
x3063.0 8			x2797.4 7	188 62	7.535 (${\frac{5}{2}}^{+}$)
x3061.1 8			x2716.4 8	150 62	90.875 (${\frac{5}{2}}^{-}$)
3056.2 6	2812.2 10	$\frac{1}{2},\frac{3}{2}$	2776.0 5	175 58	35.844 (${\frac{3}{2}}^{-}$)
			2407.2 7	143 50	404.129 (${\frac{1}{2}}^{-}$)d
x3046.5 6			x2416.5 6	159 54	404.129 (${\frac{1}{2}}^{-}$)d
x3040.0 7			x2423.0 7	91 45	404.129 (${\frac{1}{2}}^{-}$)d
x3037.0 5			x2510.3 5	369 103	321.113 (${\frac{3}{2}}^{+}$)
3017.5 8	2850.9 12	$\frac{1}{2},\frac{3}{2}$	2529.9 9	119 55	321.113 (${\frac{3}{2}}^{+}$)
			2369.8 7	199 91	481.088 (${\frac{3}{2}}^{+}$)
3009.6 7	2858.8 11	$\frac{1}{2},\frac{3}{2}$	2858.6 7	271 104	0 (${\frac{3}{2}}^{+}$)
			2537.9 7	157 63	321.113 (${\frac{3}{2}}^{+}$)
x3007.2 4			x2770.4 4	409 99	90.875 (${\frac{5}{2}}^{-}$)
x2994.6 5			x2838.0 5	294 75	35.844 (${\frac{3}{2}}^{-}$)
x2976.2 6			x2571.1 6	186 63	321.113 (${\frac{3}{2}}^{+}$)
2947.0 7	2921.4 11	$\frac{3}{2}$	2737.8 6	235 75	182.902 (${\frac{5}{2}}^{-}$)		e2912 14
			2441.0 8	155 78	481.088 (${\frac{3}{2}}^{+}$)
x2943.0 7			x2604.3 7	270 84	321.113 (${\frac{3}{2}}^{+}$)
2937.5 5	2930.9 9	$\frac{1}{2},\frac{3}{2}$	2803.8 5	306 72	126.412 (${\frac{1}{2}}^{-}$)c		e2944 14
			2609.5 6	223 75	321.113 (${\frac{3}{2}}^{+}$)
2928.1 6	2940.3 10	$\frac{3}{2}$	2932.9 6	256 70	7.535 (${\frac{5}{2}}^{+}$)		e2944 14
			2757.3 6	270 80	182.902 (${\frac{5}{2}}^{-}$)
x2925.2 7			x2537.7 7	218 78	404.129 (${\frac{1}{2}}^{-}$)d
x2918.6 6			x2766.9 6	190 68	182.902 (${\frac{5}{2}}^{-}$)
x2913.9 4			x2633.4 4	111 42	321.113 (${\frac{3}{2}}^{+}$)
2891.3 7	2977.1 11	$\frac{3}{2}$	2970.0 5	353 82	7.535 (${\frac{5}{2}}^{+}$)		e2972 15
			2655.7 7	228 89	321.113 (${\frac{3}{2}}^{+}$)
			2571.9 8	222 78	404.129 (${\frac{1}{2}}^{-}$)d
			2495.7 7	316 122	481.088 (${\frac{3}{2}}^{+}$)
x2887.1 7			x2660.2 7	230 89	321.113 (${\frac{3}{2}}^{+}$)
2881.0 7	2987.4 11	$\frac{1}{2},\frac{3}{2}$	2666.7 7	174 65	321.113 (${\frac{3}{2}}^{+}$)		e2994 15
			2581.5 7	191 74	404.129 (${\frac{1}{2}}^{-}$)d
x2876.0 9			x2809.5 9	109 61	182.902 (${\frac{5}{2}}^{-}$)
2870.1 5	2998.3 9	$\frac{1}{2},\frac{3}{2}$	2870.6 4	192 40	126.412 (${\frac{1}{2}}^{-}$)c		e2994 15
			2593.4 6	197 78	404.129 (${\frac{1}{2}}^{-}$)d
2852.8 5	3015.6 9	$\frac{1}{2},\frac{3}{2}$	2979.3 3	1189 143	35.844 (${\frac{3}{2}}^{-}$)		e3021 15
			2888.7 6	237 69	126.412 (${\frac{1}{2}}^{-}$)c
2847.1 5	3021.3 9	$\frac{1}{2},\frac{3}{2}$	3021.7 4	652 144	0 (${\frac{3}{2}}^{+}$)		3021 15
			2893.7 6	254 72	126.412 (${\frac{1}{2}}^{-}$)c
2835.7 7	3032.7 11	$\frac{3}{2}$	2941.3 6	270 83	90.875 (${\frac{5}{2}}^{-}$)		e3021 15
			2850.0 8	186 70	182.902 (${\frac{5}{2}}^{-}$)
			2712.0 7	136 58	321.113 (${\frac{3}{2}}^{+}$)
2829.4 5	3039.0 9	$\frac{3}{2}$	3003.3 3	599 102	35.844 (${\frac{3}{2}}^{-}$)		e3047 15
			2911.8 4	296 71	126.412 (${\frac{1}{2}}^{-}$)c
			2855.8 7	168 67	182.902 (${\frac{5}{2}}^{-}$)
2815.5 5	3052.9 9	$\frac{3}{2}$	3052.3 5	453 124	0 (${\frac{3}{2}}^{+}$)		e3047 15
			3017.0 3	465 92	35.844 (${\frac{3}{2}}^{-}$)
			2870.8 6	245 83	182.902 (${\frac{5}{2}}^{-}$)
2791.3 5	3077.1 9	$\frac{1}{2},\frac{3}{2}$	3040.9 3	392 85	35.844 (${\frac{3}{2}}^{-}$)		e3073 15
			2950.1 6	139 50	126.412 (${\frac{1}{2}}^{-}$)c
x2778.3 3			x2684.6 3	203 45	404.129 (${\frac{1}{2}}^{-}$)d
x2758.2 7			x2704.7 7	119 41	404.129 (${\frac{1}{2}}^{-}$)d
2740.5 4	3127.9 8	$\frac{1}{2},\frac{3}{2}$	3127.4 4	687 141	0 (${\frac{3}{2}}^{+}$)		e3135 12
			3092.6 4	338 77	35.844 (${\frac{3}{2}}^{-}$)
2696.4 5	3172.0 9	$\frac{1}{2},\frac{3}{2}$	3171.5 4	545 121	0 (${\frac{3}{2}}^{+}$)		e3187 16
			3136.3 7	135 51	35.844 (${\frac{3}{2}}^{-}$)
			2851.2 7	237 78	321.113 (${\frac{3}{2}}^{+}$)
			2766.8 4	218 51	404.129 (${\frac{1}{2}}^{-}$)d
2622.4 6	3246.0 10	$\frac{1}{2},\frac{3}{2}$	3210.2 6	168 51	35.844 (${\frac{3}{2}}^{-}$)		e3253 16
			3118.5 5	341 77	126.412 (${\frac{1}{2}}^{-}$)c
			2925.2 7	187 63	321.113 (${\frac{3}{2}}^{+}$)
2587.0 5	3281.4 9	$\frac{3}{2}$	3274.5 6	195 62	7.535 (${\frac{5}{2}}^{+}$)		e3268 16
			3245.5 5	206 56	35.844 (${\frac{3}{2}}^{-}$)
			3153.5 5	329 85	126.412 (${\frac{1}{2}}^{-}$)c
2579.8 5	3288.6 9	$\frac{1}{2},\frac{3}{2}$	3252.8 4	317 70	35.844 (${\frac{3}{2}}^{-}$)		e3291 12
			2967.5 6	194 66	321.113 (${\frac{3}{2}}^{+}$)
2563.2 5	3305.2 9	$\frac{3}{2}$	3269.4 4	297 66	35.844 (${\frac{3}{2}}^{-}$)		e3316 16
			3122.4 6	120 46	182.902 (${\frac{5}{2}}^{-}$)
2554.5 4	3313.9 8	$\frac{1}{2},\frac{3}{2}$	3277.5 3	515 86	35.844 (${\frac{3}{2}}^{-}$)		e3316 16
			2993.4 6	269 85	321.113 (${\frac{3}{2}}^{+}$)
2549.2 7	3319.2 11	$\frac{3}{2}$	3319.7 6	284 85	0 (${\frac{3}{2}}^{+}$)		e3316 16
			3312.2 7	142 50	7.535 (${\frac{5}{2}}^{+}$)
			2912.8 7	189 73	404.129 (${\frac{1}{2}}^{-}$)d
2527.2 5	3341.2 9	$\frac{3}{2}$	3334.3 6	115 43	7.535 (${\frac{5}{2}}^{+}$)		e3349 12
			3305.6 5	269 63	35.844 (${\frac{3}{2}}^{-}$)
			3157.4 5	204 63	182.902 (${\frac{5}{2}}^{-}$)
2514.3 7	3354.1 11	$\frac{1}{2},\frac{3}{2}$	3354.0 8	161 70	0 (${\frac{3}{2}}^{+}$)		e3349 12
			3225.9 6	227 62	126.412 (${\frac{1}{2}}^{-}$)c
			2948.6 9	134 64	404.129 (${\frac{1}{2}}^{-}$)d
2508.0 7	3360.4 11	$\frac{3}{2}$	3270.0 6	255 85	90.875 (${\frac{5}{2}}^{-}$)		3361 12
			2954.4 7	197 76	404.129 (${\frac{1}{2}}^{-}$)d
2446.3 6	3422.1 10	$\frac{1}{2},\frac{3}{2}$	3294.5 5	187 50	126.412 (${\frac{1}{2}}^{-}$)c		e3414 15
			3017.6 6	187 58	404.129 (${\frac{1}{2}}^{-}$)d
			2940.3 8	146 74	481.088 (${\frac{3}{2}}^{+}$)
x2428.1 7			x3119.7 8	161 60	321.113 (${\frac{3}{2}}^{+}$)
2333.0 5	3535.4 9	$\frac{1}{2},\frac{3}{2}$	3500.1 6	237 66	35.844 (${\frac{3}{2}}^{-}$)
			3407.7 3	337 67	126.412 (${\frac{1}{2}}^{-}$)c
2104.7 6	3763.7 10	$\frac{1}{2},\frac{3}{2}$	3763.3 5	232 78	0 (${\frac{3}{2}}^{+}$)		e3759 13
			3443.0 7	103 46	321.113 (${\frac{3}{2}}^{+}$)

Model	CT		BSFG
Parameter	$E_0$ (MeV)	$T$ (MeV)	$a$ (MeV-1)	$E_1$ (MeV)
Parameters from egidy2005	$-2.06\pm 0.29$	$0.61\pm 0.03$	$17.76\pm 0.28$	$-1.08\pm 0.13$
Fitted to This work 1 in Fig. LABEL:culm(a)	-	-	$3.51\pm 0.28$	$-12.09\pm 1.24$
Fitted to This work 1 in Fig. LABEL:culm(b)	-	-	$12.73\pm 0.16$	$-3.49\pm 0.07$

Equations

$$\text{max}(J_i-L,J_f-L)\le J\le \text{min}(J_i+L,J_f+L),$$

$$N(E_x)={\int }_0^{E_x}\rho (E)dE,$$

$${\rho }_{CT}(E,J)=f(J){\rho }_{CT}(E)=f(J)\frac{1}{T}{e}^{(E-E_0)/T},$$

$${\rho }_{BSFG}(E,J)=f(J){\rho }_{BSFG}(E)=f(J)\frac{e^{2\sqrt{a(E-E_1)}}}{12\sqrt{2}\sigma a^{1/4}(E-E_1{)}^{5/4}},$$

$$f(J)=e^{-J^2/2{\sigma }^2}-e^{-(J+1{)}^2/2{\sigma }^2}\simeq \frac{2J+1}{2{\sigma }^2}{e}^{-(J+\frac{1}{2})/2{\sigma }^2},$$

Full text

I Introduction

The energy-level properties of excited nuclei (called the nuclear level scheme), which include the level energies, spins, parities, and gamma-rays associated with the excited levels, are important for the study of nuclear structure physics, nuclear reactions, and nuclear astrophysics. The level schemes of nuclei in the mass region $A\sim 150\div 154$ are of particular interest because the nuclear deformation in this region was predicted to change drastically with only slight variations of $A$ 1969Sm04 ; 1979Re04 . Nuclei in this mass region are also called transitional nuclei. For example, 150Sm and 152Sm have very different level schemes as the former has the vibrational/quasi-vibrational characteristics, whereas the latter follows the rotational ones 1968Lure . Similarly, the level spectrum of 152Sm shows both rotational and vibrational behaviors, whereas that of 154Sm exhibits the strong rotational properties, indicating that this nucleus is strongly deformed 1964Robert . Moreover, two odd nuclei, 151Sm and 153Sm, which fall, respectively, between the two sets (150Sm, 152Sm) and (152Sm, 154Sm) are expected to be affected by the interplay between the rotational and vibrational bands 1971Be41 . Therefore, the level schemes of 151,153Sm odd nuclei have been an interesting subject of many experimental and theoretical studies. The present paper focuses on the experimental study of the level scheme of 153Sm by using thermal neutron-capture reaction.

The level scheme of 153Sm has been studied by using different nuclear reactions and techniques Helmer2006 and all the experimental data have been compiled in the ENSDF library ENSDF . For instance, the level scheme of 153Sm at the low-energy(spin) region (below 1.53 MeV) was studied by using the $\beta^{-}$ decay of 153Pm as well as the decay from the isomeric state of 153Sm to its ground state 1971KiZC ; 1983MaYP ; 1995Gr19 ; 1997Gr09 . These experiments detected in total 25 excited levels, 17 of which have the unique spin values within the interval of $[\frac{1}{2},\frac{9}{2}]\hbar$. The high-spin part in the level scheme of 153Sm was measured by using the heavy-ion capture reactions, in which a total number of 28 excited levels, 25 of which have the unique spin values falling into the range of $[\frac{11}{2},\frac{41}{2}]\hbar$, was reported 1979Re04 ; 1999As05 ; 2000Ha59 . However, the above experiments have not covered the excited levels, whose energy and spin are in the regions of $[1.5,4.0]$ MeV and $[\frac{1}{2},\frac{3}{2}]\hbar$, respectively. In these regions, several transfer reactions such as ${}^{151}(t,p)$ 2005Bu21 , 152Sm$(d,p)$ 1965Ke09 ; 1972Ka07 ; 1997GoZn ,154Sm$(d,t)$ 1971Be41 ; 1972Ka07 ; 1997GoZn , 154Sm$(p,d)$ 1997GoZn ; 1997Bl11 , 152Sm($\alpha,^{3}$He) 1984Li02 , 154Sm(3He, $\alpha$) 1997GoZn , and 154Eu($t,\alpha$) 1985Ma26 have been employed and a considerable number of excited levels of 153Sm within the spin range of $[\frac{1}{2},\frac{11}{2}]\hbar$ has been explored. Most importantly, by using the 152Sm$(d,p)$ reaction, 132 excited levels below 3.929 MeV and 56 excited levels below 1.991 MeV in the level scheme of 153Sm have been deduced in Refs. 1965Ke09 and 1972Ka07 , respectively. Although, the data reported in Refs. 1965Ke09 and 1972Ka07 agree with each other, their uncertainties are quite high (about 10 keV or higher). The reason is that within the framework of the transfer reactions, the excited levels are indirectly deduced from the energy and momentum distributions of the reaction products (charged particles), instead of the direct way, that is, from the gamma transitions of the excited levels. The latter were also not reported in Refs. 1965Ke09 and 1972Ka07 .

Apart from the above ion-induced experiments, the neutron-captured reactions also play an important role in the construction of the 153Sm level scheme. In fact, by using the ($n_{th},\gamma$) and ($n$ = 2 keV, $\gamma)$ reactions ($n_{th}$ means the thermal neutron with energy of 0.025 eV), Refs. 1971Be41 ; 1969Sm04 ; 1969Re04 ; 1997GoZn have thoughtfully investigated the level scheme of 153Sm by means of the bent-crystal, conversion-electron, and Ge detector spectrometers. For the latter, the first two spectrometers, which were used to measure the low energy gamma-rays, focused on the low-energy part (below 0.4 MeV) of the 153Sm level scheme, whereas the last one was used to detect the high-energy gamma rays and to consequently deduce the feeding levels corresponding to the observed gamma rays. Moreover, through the gamma spectrum measured by the Ge detectors, 35 gamma rays emitted from the compound state of 153Sm via ($n_{th},\gamma$) reaction were reported in Refs. 1971Be41 ; 1969Sm04 ; 1969Re04 . Similarly, Ref. 1997GoZn has detected 31 gamma rays via ($n$ = 2 keV, $\gamma)$ reaction. Many excited levels, whose energies range from 0 to approximately 2.7 MeV, were also deduced from the gamma rays detected in Ref. 1997GoZn . In general, the number of gamma rays that can be detected by the conventional Ge detector spectrometer is restricted by the high Compton background of the gamma spectrum as well as the energy resolution of the Ge detector. Besides, the gamma spectrum of 153Sm obtained from the ($n,\gamma$) reaction is always influenced by 150Sm because the thermal neutron-capture cross section of 149Sm is extremely higher than that of 152Sm (See e.g., Table 1).

Given the limitations of the works mentioned above, it is necessary to improve the level scheme of 153Sm, especially in the energy region from 0.5 MeV to about 5.0 MeV. One of the possibilities is to perform the 152Sm($n_{th},\gamma$) reaction using an advance $\gamma-\gamma$ coincidence technique together with the Ge(Li) detectors (also called the (n, 2$\gamma$) technique or the method of digital summation amplitudes of coincident pulses) boneva1991 . This technique, which has advantages in identifying the correlated gamma transitions and in subtracting most of the Compton background, allows us to detect the two-step gamma cascades (TSC) decayed from the compound state to the low-energy final levels and can therefore be used to deduce many new excited levels in 153Sm within the energy region from 0.5 MeV to approximately 5.0 MeV and the spin range of $[\frac{1}{2},\frac{3}{2}]\hbar$. Indeed, by using the above technique, we have successfully studied the updated level scheme of 172Yb via 171Yb($n_{th},\gamma$) reaction anh2017 . In particular, we have detected in the level scheme of 172Yb several new excited levels and the corresponding gamma transitions, whose data do not currently exist in the ENSDF library, especially in the intermediate energy region from 3 to 5 MeV.

The goal of the present paper is to update the level scheme of 153Sm via the ($n_{th},\gamma$) reaction by using the $\gamma-\gamma$ coincidence technique. The energy and spin regions to be covered by this experiment are $[0.52,5.3]$ MeV and $[\frac{1}{2},\frac{3}{2}]\hbar$, respectively. In addition, by combining our newly updated levels with those presently existed in the ENSDF library, we are able to construct the new total and partial (within spin range of $[\frac{1}{2},\frac{3}{2}]\hbar$) cumulative numbers of discrete levels, which are latter used to test the predictive power of various nuclear level density (NLD) models. At the same time, these new cumulative curves have also been compared with those extracted from the NLD data obtained by using the Oslo method OsloMethod .

II Experimental Method

The 152Sm($n_{th},\gamma$) reaction was carried out at Dalat Nuclear Research Institute (Vietnam) using the thermal neutron beam from the tangential channel of Dalat Nuclear Research Reactor. The thermal neutron beam, which was obtained by using the filtered technique, has the size and flux at the irradiated position to be equal to 2.5 cm and 1.7 $\times$ 105 n.cm*-2*.s*-1*, respectively. This beam configuration is sufficient for the present experiment as discussed e.g., in Ref. anh2017 . The experimental setup and measurement using the $\gamma-\gamma$ coincidence spectrometer with two HPGe detectors are the same as those presented in Ref. anh2017 (except the target nucleus), so we do not repeat them here.

The target nucleus 152Sm is in the form of a 583 mg Sm2O3 powder. This target, which was put in a plastic bag, was then measured at the center of the thermal neutron beam during approximately 661 hours. The isotopic content of the target, which is provided by the JSC Isotope Supplier with the quality certificate being given under the Contract No. 704/08625142/25/30-16, together with the thermal neutron-capture cross sections ($\sigma_{th}$) of all the isotopic components ncs are given in Table 1.

Table 1 shows that 144,148,154Sm isotopes have the values of both concentration and $\sigma_{th}$ being significantly smaller than those of 152Sm. Consequently, their influence on the spectroscopic data is negligible. For 147,150Sm isotopes, although their $\sigma_{th}$ values are comparable with that of 152Sm, their impact on the spectroscopic data is still small because of their tiny percentages. The only samarium isotope, which has a considerable influence on the spectroscopic data, is 149Sm because it has the noticeable $\sigma_{th}$ value, namely $\sigma_{th}$ of 149Sm is $\sim$ 198 times higher than that of 152Sm. Therefore, despite the percentage of 149Sm is $\sim$ 759 times less than that of 152Sm, its contribution to the coincidence events caused by the thermal neutron capture of 149Sm is only $\sim$ 3.8 times less than that of 152Sm, implying that approximately 20% of all the detected coincidence events will be affected by the excited compound 150Sm nucleus. Fortunately, the two-step cascades caused by 150Sm can be distinguished from those of 153Sm by using the $\gamma-\gamma$ coincidence method because their summation energies (the total energy of two gamma rays) are different. For instance, the summation energies of the cascades of 150Sm detected within the present experiment range from $\sim$ 6.0 MeV to its neutron binding energy $B_{n}=$ 7.9867 MeV AME2016 , whereas those of 153Sm vary from $\sim$ 5.2 MeV to 5.87 MeV as clearly seen in Fig. 1.

For every detected coincident events, the energies absorbed by two HPGe detectors are recorded. The gamma cascades, which come from the decays of the compound state, go through different intermediate levels, and reach the ground state and some defined final levels, can be identified in the form of appropriate peaks appearing in the summation spectrum. The latter is obtained by counting the number of events per an interval of total energy absorbed by two HPGe detectors.

The most instructive part of the summation spectrum of 153Sm is shown in Fig. 1. In this figure, all the gamma cascades decayed from the compound state to the ground state and 15 final states, whose energies are 7.535, 35.844, 90.875, 126.412, 127.298, 182.902, 276.713, 321.113, 356.686, 362.286, 404.129, 405.470, 414.924, 450.050 and 481.088 keV111It should be noted that the very precise energy values of the final levels given in the present paper are taken from Ref. Helmer2006 ., can be identified based on their corresponding peaks. By gating on the appropriate peak, the TSC spectrum corresponding to the gamma cascades from the compound state to a given final level is obtained. Figure 1 also shows some overlaps between different groups of states, whose energies are not much different, e.g. (0, 7.535 keV), (414.924, 404.129, and 405.470 keV), etc. The gamma cascades coming from these overlap peaks are indistinguishable because of the restricted energy resolution of the HPGe detectors used in the present experiment. However, these overlaps can be possibly reduced by a special selection of the gating window as illustrated in Fig. 2. It can be seen in this Fig. 2 that an overlapped peak of two states can be fitted by two Gaussian functions, whose width and centroid position are different. Thus, the overlapped region can be easily identified if the gating window is divided into two regions. The first region is set between the lines (1) and (2) corresponding, respectively, to the head-tail and maximum positions of first Gaussian. The second region is chosen between the lines (3) and (4), which correspond to the maximum and end-tail positions of the second Gaussian, respectively. Once the overlapped region is identified (see the overlapped area in Fig. 2), its contribution can be easily reduced from the TSC spectrum. As a result, the contribution of the overlapped regions to the obtained TSC spectra is found to be less than 5%. However, it should be noted that the above approach can not be applied if energies of the overlapped peaks are notably close to each others, namely the different between energies of two peaks is smaller than 0.8 FWHM (Full Width at Half Maximum), e.g. the following pairs of final levels (126.412, 127.298) keV and (404.129, 405.470) keV.

All the measured TSC spectra are shown in Fig. 3. Due to the low statistics, the TSC spectra corresponding to the following final levels 276.713, 356.686, 362.286, and 450.050 keV have not been analyzed yet. Despite the energy resolutions of the two HPGe detectors used in the present experiment are slightly different, the obtained TSC spectra are mirror symmetry because an algorithm for improving the digital resolution resolution has been applied. The vicinity regions around each summation peak are gated to create a corresponding background spectrum. The latter is then subtracted from the spectrum obtained from the gating of the peak region, thus leading to some negative values in the TSC spectra in Fig. 3.

A pair of peaks, which are symmetric within a TSC spectrum, represents a gamma cascade. The peak positions and areas correspond to the transition energies and intensities, respectively. In order to construct the nuclear level scheme, we assume that the gamma transitions, which appear in more than one TSC spectrum, are considered to be the primary transitions. In addition, a transition is also considered as primary if it is currently determined as primary in the ENSDF library ENSDF .

As for the spin of the levels, the possible spins of an observed intermediate level are often evaluated by using the following formula

[TABLE]

where $J_{i},J$, and $J_{f}$ are spins of the initial, intermediate, and final levels, respectively, whereas $L$ is the multipolarity. Within the present work, we assume that all the observed transitions are dipole ($L=1$). This assumption is made because the probability of detecting the dipole transition is much higher than that of the quadrupole ($L=2$) blatt1991book .

III Results and Discussion

III.1 Level scheme of 153Sm

We have identified in total 576 gamma transitions corresponding to 386 gamma cascades, which are associated with the decays from the compound state to the ground state and 11 final levels (see Table LABEL:tab2). The latter are 7.535 ($\frac{5}{2}^{+}$), 35.844 ($\frac{3}{2}^{-}$), 90.875 ($\frac{5}{2}^{-}$), 126.412 ($\frac{1}{2}^{-}$), 127.298 ($\frac{3}{2}^{-}$), 182.902 ($\frac{5}{2}^{-}$), 321.113 ($\frac{3}{2}^{+}$), 404.129 ($\frac{1}{2}^{-}$), 405.470 ($\frac{3}{2}^{-}$), 414.924 ($\frac{1}{2}^{+}$), and 481.088 ($\frac{3}{2}^{+}$) keV. Based on these observed cascades, we have determined 103 primary gamma transitions corresponding to 103 intermediate levels and 299 secondary transitions emitted from these levels. Among the above primary transitions, 99 transitions have been deduced since they appear in more than one TSC spectrum. The remain 4 transitions, whose the energies are 4329.1, 4420.1, 4769.6, and 5133.2 keV, are also considered as the primary ones despite that they appear in only one TSC spectrum because these transitions are found to be the same as the primary transitions that currently exist in the ENSDF library Helmer2006 .

Since the compound state of 153Sm has the spin of $\frac{1}{2}\hbar$, by using Eq. (1) together with an assumption that all the observed transitions are dipole, we are able to tentatively assign an unique spin value of $\frac{3}{2}\hbar$ for 53 intermediate levels, which correspond to the gamma transitions emitted from the compound state to 3 final levels with the spins of $\frac{5}{2}\hbar$, namely the 7.535 ($\frac{5}{2}^{+}$), 90.875 ($\frac{5}{2}^{-}$), and 182.902 ($\frac{5}{2}^{-}$) keV levels. For the remain 50 levels, which relate to the gamma transitions emitted from the compound state to the final levels with the spin of $\frac{1}{2}\hbar$ or $\frac{3}{2}\hbar$, their spin values can not be uniquely deduced. Consequently, a possible spin range from $\frac{1}{2}\hbar$ to $\frac{3}{2}\hbar$ has tentatively been assigned to these levels.

The assumption that all the observed transitions are dipole is made based on the following experimental evidences. First, among all the transitions coming from the compound state (see the ($n,\gamma$) datasets for thermal and 2-keV neutrons in Ref. Helmer2006 ), we found only 2 transitions which are not dipole, namely the 5506.4 and 5861.4 keV transitions to the 362.286 ($\frac{5}{2}^{+}$) and 7.535 ($\frac{5}{2}^{+}$) keV levels, respectively. These transitions, however, have considerably low intensities compared to those obtained from other primary transitions. Moreover, the 5506.4 keV transition has solely found in Ref. 1969Sm04 , whereas that of 5861.4 keV has only detected in the form of a doublet with the strong transition of 5868.4 keV in Refs. 1969Sm04 ; 1969Re04 ; 1971Be41 , which has not been reproduced within the framework of ($n,\gamma$) experiment with 2-keV neutron 1997GoZn . Second, within the low-excitation energy of 153Sm level scheme, the quadrupole transitions have rarely been reported. In fact, there are only few quadrupole transitions, which currently existed in the ENSDF library, such as the 223.173 and 278.17 keV transitions coming from the 276.713 and 405.470 keV levels, respectively. They all together have lower energy than the energy threshold of the present work (520 keV for both transition and excitation energy). These evidences apparently ensure the validity of the assumption above and consequently the reliability of the spin assignment within the present work, despite that the assumption is still restrictive and the spin assignment within the present work can not be determined as the definite values.

By comparing the 153Sm level scheme obtained within the present work with that extracted from the ENSDF library Helmer2006 , we have realized that 29 primary gamma transitions and 42 intermediate levels are found to be the same within their uncertainties, whereas only 8 secondary transitions are the same with those existed in the ENSDF library. The remain 74 primary gamma transitions, 61 intermediate levels, and 291 secondary transitions are therefore considered as the new data obtained within the present experiment.

In particular, the 153Sm level scheme obtained within the present work agrees well with that obtained within the previous studies using the same 152Sm($n_{th},\gamma$) reaction 1997GoZn ; 1971Be41 ; 1969Sm04 ; 1969Re04 . For the energy region below 5300 keV, which is the maximum gamma energy that can be detected within the present experiment (because the energy threshold of detectors were set to be around 520 keV), we have reproduced 19 over 24 primary transitions that were previously reported in Refs. 1997GoZn ; 1971Be41 ; 1969Sm04 ; 1969Re04 . Among the 5 unreproduced transitions, 2 transitions, whose energies are 5220.4 and 5283.9 keV, were reported in Ref. 1971Be41 , whereas 2 transitions with the energies of 4850 and 4864.0 keV were detected in Ref. 1969Sm04 . These transitions were found very long time ago and have not been reproduced by other experiments. The remain 4505.6 keV transition was reported with a slightly different energy of 4506.6 $\pm$ 1.0 keV in Ref. 1969Re04 or 4505.8 $\pm$ 0.4 keV in Ref. 1971Be41 , or 4506.5 $\pm$ 0.6 keV in Ref. 1969Sm04 . This 4505.6 keV transition might be therefore the same as the 4507.4 $\pm$ 0.4 keV transition observed within the present work as well as the 4507.41 keV transition obtained from the ($n,\gamma$) experiment with the 2-keV neutron source in Ref. 1997GoZn . In general, we have reproduced 22 over 26 levels that were reported by the previous ($n_{th},\gamma$) experiments within the excitation energy above 600 keV in Refs. 1997GoZn ; 1971Be41 ; 1969Sm04 ; 1969Re04 .

The result of the 153Sm level scheme obtained within the present work also agrees well with the neutron capture experiment using 2-keV neutron source, namely 22 over 24 primary transitions within the gamma energy of 520 to 5300 keV and 23 over 29 levels within the excitation energy region of 600 to 2000 keV reported in Ref. 1997GoZn have been replicated within the present experiment. Among the remain unreproduced levels, 4 levels, whose energies are 1675.8, 1723.5, 1737.5, and 1751.4 keV, have been determined in Ref. 1997GoZn without any populating gamma transitions. In addition, all the levels reported in Ref. 1997GoZn with the assigned spins of $\frac{1}{2}\hbar$ or $\frac{3}{2}\hbar$ are fully in agreement with those deduced from the present study.

Furthermore, our data also go along with those obtained within the ion-induced experiments, in particular the 152Sm($d,p$) 1965Ke09 ; 1972Ka07 ; 1997GoZn , 154($p,d$) 1997GoZn ; 1997Bl11 , and 154($d,t$) 1972Ka07 ; 1997GoZn ; 1971Be41 reactions. Below 2000 keV, 24 excited levels found in the present work are supported by at least one of the experiments employing the ion-induced reactions. Similarly, 44 excited levels found within the present experiment agree with those extracted from the ion-induced reactions within their uncertainties (see the excited levels with the superscript denotation ”e” in Table LABEL:tab2). It should be noted here that the uncertainties of the data obtained within the ion-induced experiments are often in the range of 8 to 18 keV, which are much larger than those obtained within the present work. Therefore, we consider that two levels are the same only if their discrepancy is less than 1.5 keV, that is, if a level deduced from the present experiment agrees with that deduced from the ion-induced experiments but the discrepancy between the two levels is larger than 1.5 keV, it is considered as the new level.

ENSDF: data taken from the ENSDF library Helmer2006 .

$E_{1}$: energy (in keV) of the primary gamma transition.

$E_{2}$: energy (in keV) of the secondary gamma transition.

$E_{i}$: energy (in keV) of the intermediate level.

$I_{\gamma\gamma}$: absolute intensity of the cascade normalized to 106 decays. Uncertainties of the normalization factors are not taken into account.

$E_{f}$: energy (in keV) of the final level. Spin and parity of the final level are given in the parentheses.

$J_{i}$: tentative spin (in $\hbar$) of the corresponding level.

Throughout the table, the uncertainty for numeric values is given next to the corresponding value (in the $italic$ type) and referred to the last digits of the value, e.g. 12.1 23 means 12.1 $\pm$ 2.3.

The experimental data within the present work, which agree with those existed in the ENSDF library, are highlighted in the bold type.

a data taken from the ($n,\gamma$) with thermal and 2-keV neutron datasets in Ref. Helmer2006 .

b data taken from the Adopted Level dataset in Ref. Helmer2006 .

c unresolved final levels: 126.412 ($\frac{1}{2}^{-}$) or 127.298 ($\frac{3}{2}^{-}$).

d unresolved final levels: 404.129 ($\frac{1}{2}^{-}$) or 405.470 ($\frac{3}{2}^{-}$).

e energy of the observed level, which agrees with those obtained from the ion-induced 152Sm($d,p$) and/or 154($p,d$) and/or 154($d,t$) reactions within their uncertainty. It is noted that the superscript denotation ”e” is not marked if the discrepancy between the observed level and that presented in the ENSDF library is less than 1.5 keV.

f the values of the 630.20 keV level and its spin are taken from the ($n,\gamma$) experiments.

g the spin value of $\frac{1}{2}\hbar$ was assigned to the 695.80 keV level in the ENSDF library based on the strong supports from the $l$-transfer and vector analyzing power in the $(d,t)$ particle-transfer reaction, whereas the present work suggests a different spin value, namely $\frac{3}{2}\hbar$. Our suggestion for this level is made based on its weak 604.8 keV dipole transition to the 90.875 keV ($\frac{5}{2}^{-}$) state. In the case the 604.8 keV transition is quadrupole, the spin of $\frac{1}{2}\hbar$ must be assigned to the 695.7 keV level found within the present work.

h this level can not be distinguished from the 734.7 keV ($\frac{1}{2}^{+}$) level within the present experiment.

i this level can not be distinguished from the 984.3 keV ($\frac{3}{2}^{-}$) level within the present experiment.

j the observed levels of 2494.7 10 and 2497.1 9 keV both agree with the 2496.6 12 keV state within their experimental uncertainties. Thus, there is a possibility that these three levels are all the same.

x the gamma cascades, which we are not able to identify as the primary transitions within the present work.

Table LABEL:tab2 presents the absolute intensities normalized to 106 captures together with the statistical uncertainties of all 386 measured cascades. The normalization factor is determined based on the absolute intensities of 4697.2 and 5117.8 keV primary transitions (i.e., the 4697.4 and 5118.3 keV transitions within the present work) taken from the ENSDF data Helmer2006 together with their branching ratios. The latter are determined from the gating spectrum of the primary transitions mentioned above. Since the energy threshold of the present experiment is 520 keV, we are not able to identify the branches, whose energy of the secondary transition is less than 520 keV. Therefore, our cascade intensities may contain a certain systematic error.

In general, the present experiment reproduces most of the ENSDF data obtained from the neutron capture and ion-induced reactions. This consistency obviously proves the reliability of the data obtained within the present study.

Thanks to the coincidence technique, the influence of 150Sm on the spectroscopic information of 153Sm, which limits the number of data obtained from the neutron-capture experiment using the conventional HPGe detector 1971Be41 ; 1969Sm04 ; 1969Re04 , has been considerably reduced within the present experiment. This technique also reduces the peak overlaps, which are immensely common in analyzing the conventional prompt gamma spectra, especially for nuclei with the complicated level scheme such as in the case of 153Sm. The reason is that the coincidence technique is able to detect only the intermediate level in a narrow spin range from $J_{i}-1$ to $J_{i}+1$ ($J_{i}$ is the spin of the compound state) and the detected gamma transitions are distributed to the multiple TSC spectra. As a result, we are able to detect more important information on the level scheme of 153Sm, which have not currently existed in the ENSDF library.

III.2 Cumulative number of levels

III.2.1 Experimental cumulative number of levels

Since several new energy levels have been detected within the present experiment, we are able to construct the total and partial cumulative numbers of levels, which are, by definition, the numbers of excited levels fall within the specific energy and spin ranges. These cumulative numbers are constructed by combining the adopted levels taken from the ENSDF Helmer2006 with those obtained within the present work (Table LABEL:tab2). For the latter, however, there are unassigned intermediate levels corresponding to 87 gamma cascades as shown in Table LABEL:tab2 with the superscript denotation ”x”. Therefore, we have constructed two cumulative curves denoted by “This work 1” and “This work 2” (see Fig. LABEL:cul). “This work 1” is created by assuming that the gamma transitions in each of 87 cascades with the higher energies are considered as the primary transitions, whereas those with lower energies correspond to the secondary ones. “This work 2” is generated by using the opposite assumption, namely the gamma transitions with lower (higher) energies are considered as the primary (secondary) ones. It is obvious that “This work 1” is always higher than “This work 2”, regardless of their total or partial cumulative curves because “This work 1” contains the primary gamma transitions, whose energies are higher than those in “This work 2” (Fig. LABEL:cul). Here, it should be noted that the assumption for “This work 1” should be much more reliable than that for “This work 2” because within the two-step cascades, one often observes the primary transition, whose energy is higher than that of the secondary one (see e.g. the data reported in the ENSDF library ENSDF ). Consequently, the real cumulative curve should probably be very close to “This work 1”.

The total and partial cumulative numbers of levels within the present work are also compared with those obtained by using the NLD data in Ref. Oslo . The total cumulative curve in this case is calculated by using the conventional formula gcmodel

[TABLE]

where $\rho(E)$ is the experimental NLD taken from Ref. Oslo . As for the partial cumulative curve for the spin range $J=[\frac{1}{2},\frac{3}{2}]\hbar$, it should be calculated using the same Eq. (LABEL:ne_total) but the $J$-dependent NLD $\rho(E,J)$ must be used instead of the total NLD $\rho(E)$. However, there exists in literature only the total NLD extracted by using the Oslo method $\rho(E)$ in Ref. Oslo . The latter was extracted from the gamma spectra of the 154Sm$(p,d\gamma)^{153}$Sm reaction, which were later normalized using the discrete levels taken from the ENSDF library ENSDF as well as the NLD data at the neutron binding energy (see e.g., Fig. 3 of Ref. Oslo ). Therefore, in order to estimate the $\rho(E,J)$ values, we have manually multiplied $\rho(E)$ with a factor, which is determined as the ratio between the number of levels with spins $J=\frac{1}{2}$ and $\frac{3}{2}\hbar$ and the total number of levels existed in the ENSDF library Helmer2006 . This factor is found to be about 0.27 for 153Sm. The obtained $\rho(E,J)$ is then used to calculate the partial cumulative curve $N(E_{x},J)$ for $J=[\frac{1}{2},\frac{3}{2}]\hbar$. For the sake of simplicity, the corresponding results, namely the total and partial cumulative curves estimated using the NLD data in Ref. Oslo , are called the estimated data/curves hereafter. It is seen in Figs. LABEL:cul(a) and (b) that such an estimation seems to be valid for the low-energy region (below 1 MeV) as both estimated curves for the total and partial cumulative numbers of levels are in excellent agreement with the ENSDF data. It is obvious that the spin distribution is not constant over the excitation energy. Thus, the estimated data presented in Fig. LABEL:cul(b) may not be corrected in the high-energy region above 1 MeV. Since the spin distribution changes very slightly when the excitation energy is low, we believe that our deduction is acceptable with a negligible error for the energy region from 1 MeV to 2 MeV. It is interesting to see in Fig. LABEL:cul(b) that “This work 1” almost coincides with the estimated data in the energy region from 0 to about 1.8 MeV, above which the data obtained from our estimation might be no longer valid. “This work 2” and ENSDF curves agree with the estimated data up to about 1 MeV only. This result supports strongly the validity of the assumption for “This work 1”, which is the most common assumption used in the two-step cascade experiments as explained above. This assumption can also be confirmed by comparing the total NLD in Ref. Oslo with those obtained from the ENSDF, “This work 1”, and “This work 2” (Fig. LABEL:nld). It is clearly to see in Fig. LABEL:nld that the total NLDs taken from the ENSDF and “This work 2” only agree with the data of Ref. Oslo below 1 MeV, whereas the agreement between “This work 1” and Ref. Oslo ’s data is extended up to about 1.2 MeV, indicating by two arrows in Fig. LABEL:nld.

The results obtained from ”This work 1” as shown in Figs. 4 and 5 indicate two significant contributions of the new levels found within the present work. The first contribution is that for the total NLD, the maximum excitation energy $E_{\rm max}$, defined as the energy threshold below which most of the excited levels have been observed, is now extended to about 1.2 MeV, instead of 1.0 MeV as that obtained from the ENSDF data Helmer2006 (Figs. LABEL:cul(a) and LABEL:nld). The second contribution is associated with the value of $E_{\rm max}$ for the spin range of [$\frac{1}{2},\frac{3}{2}$]$\hbar$, which has been increased up to about 1.8 MeV (Fig. LABEL:cul(b)). It is evident that the NLD calculated by counting the numbers of discrete levels has been widely considered as the most reliable data, which are often used for the normalization of the experimentally extracted data OsloMethod as well as different NLD model calculations hfbcs ; hfb . However, the present ENSDF library provides the reliable NLD up to about 1 MeV only. By including our new data, we are able to obtain, for the first time, the reliable NLD data up to about 1.2 MeV and 1.8 MeV for the total and partial (within the spin range of [$\frac{1}{2},\frac{3}{2}$]$\hbar$) NLDs, respectively. This second contribution is therefore the most important contribution of the present work.

III.2.2 Comparison with theoretical models

The cumulative number of levels is very helpful for verifying the predictive power of the NLD models. In Fig. LABEL:culm, we compare our experimental cumulative curve (This work 1) with two phenomenological NLD models, namely the back-shifted Fermi gas (BSFG) and constant temperature (CT). The functional forms of these two models are taken from Ref. egidy1988 , that is

[TABLE]

where $\sigma_{CT}=0.98A^{0.29}$ and $\sigma_{BSFG}=0.0146A^{5/3}\frac{1+\sqrt{1+4a(E-E1)}}{2a}$ are the spin cut-off parameters with $E_{1}$ and $a$ being the back-shifted energy and level density parameters, respectively. Two parameters $E_{0}$ and $T$ in Eq. (LABEL:ct) are the energy shift and constant temperature, whereas the function $f(J)$ in Eq. (LABEL:fj) is the conventional spin distribution of the NLD gcmodel . The free parameters $a,E_{1},E_{0}$, and $T$ of the BSFG and CT are often adjusted to fit the total cumulative number of levels as well as the NLD determined from the experimentally averaged neutron-resonance spacing data ($D_{0}$ value) egidy2005 . The values of these free parameters taken from Ref. egidy2005 (see also Table LABEL:tab3) were used to calculate $\rho_{CT}(E)$, $\rho_{BSFG}(E)$, $\rho_{CT}(E,J)$, and $\rho_{BSFG}(E,J)$ ($J=$[$\frac{1}{2},\frac{3}{2}$]$\hbar$). The total and $J$-dependent cumulative numbers of levels are then calculated making use of Eq. (LABEL:ne_total). The results obtained shown in Fig. LABEL:culm(b) indicate that the CT model with parameters taken from Ref. egidy2005 fits well to our experimental data (This work 1) for the spin range of [$\frac{1}{2},\frac{3}{2}$]$\hbar$, but it is higher than our experimental total cumulative curve (Fig. LABEL:culm(a)). The reason is that the parameters of the CT model taken from Ref. egidy2005 were given based on the analysis of 21 excited levels below 0.49 MeV within the spin range of [$\frac{1}{2},\frac{9}{2}$]$\hbar$ (close to the spin range of [$\frac{1}{2},\frac{3}{2}$]$\hbar$ within the present work), whereas below 0.49 MeV, there must be in total 37 excited levels within a much larger spin range of [$\frac{1}{2},\frac{19}{2}$]$\hbar$ as in the ENSDF library Helmer2006 . Consequently, while the CT model describes well the experimental $J$-dependent cumulative curve, it is unable to describe the total one. For the BSFG model with the free parameters taken from the same Ref. egidy2005 , it completely fails to describe both the total and $J$-dependent experimental cumulative curves (see Fig. LABEL:culm). The above results of the CT and BSFG models clearly demonstrate that the prediction of the phenomenological NLD models depends strongly on the values of their free parameters. For instance, by re-fitting the results of the BSFG model to our total and $J$-dependent experimental cumulative data, we obtain the different sets of free parameters as reported in Table LABEL:tab3. To obtain a reliable predicting power, one should therefore use the microscopic NLD models instead of the phenomenological ones.

Within the present paper, three microscopic NLD models have been selected, namely the Hartree-Fock BCS (HFBCS) hfbcs , the Hartree-Fock-Bogoliubov plus combinatorial method (HFBC) for the positive (HFBC $\pi^{+}$) and negative (HFBC $\pi^{-}$) parities hfb , and the recent exact pairing plus independent-particle model at finite temperature (EP+IPM) epipm . The HFBCS and HFBC data are accessible from RIPL-2 ripl2 and RIPL-3 ripl3 , respectively. These models have been considered to be the most up-to-date microscopic theoretical models for the NLD. Figure LABEL:nld1 shows the total NLD $\rho(E)$ obtained within the HFBCS, HFBC, and EP+IPM in comparison with the experimental data. This figure indicates that while the HFBCS agrees with the experimental data only in the very low-energy region (below 0.5 MeV), both the HFBC and EP+IPM offer a good fit to the measured data. Moreover, the HFBC can not describe the data below 0.5 MeV, whereas the EP+IPM, in general, agrees with both low- and high-energy data. Consequently, one can easily see in Fig. LABEL:culm1 that only the EP+IPM can describe both the experimental total and partial cumulative curves. This result of EP+IPM does not go beyond our expectation because this model has successfully been used to describe the NLD data of not only hot 170-172Yb epipm and 60-62Ni epipm1 nuclei but also several hot rotating $A\sim 200$ isotopes epipm2 . In addition, the EP+IPM does not use any fitting parameters as discussed in Refs. epipm ; epipm2 ; epipm3 , whereas the HFBCS and HFBC often employ some fitting parameters (see e.g., Eqs. (17) and (18) of Ref. hfbcs or Eq. (25) of Ref. hfb ) to the experimental total cumulative data at low energy and the $D_{0}$ value at energy $E=B_{n}$. The above results, once again, confirm the microscopic nature and universality of the EP+IPM NLD model proposed in Ref. epipm . In other words, the presently updated data provide a good test for both phenomenological and microscopic NLD models.

IV Conclusion

The present paper studies the excited levels of 153Sm nucleus populated in the thermal neutron-capture reaction using the $\gamma-\gamma$ coincidence technique and high resolution HPGe detectors. The coincidence technique together with the highly enriched target for 152Sm isotope allow us to significantly eliminate the influence of 150Sm excited nucleus in the observed gamma spectrum. In addition, the statistics of the measured data are rather high within the framework of coincident measurements. As a result, we are able to detect many new energy levels and their corresponding gamma transitions, namely 74 primary gamma transitions, 61 intermediate levels, and 291 secondary transitions. The tentative spin value of 53 observed levels is found to be $\frac{3}{2}\hbar$, whereas the remain levels are tentatively adopted to be in the spin range of $[\frac{1}{2},\frac{3}{2}]\hbar$.

By combining the updated energy levels with those obtained from the ENSDF library, we have constructed the new total and partial (within the spin range of $[\frac{1}{2},\frac{3}{2}]\hbar$) cumulative numbers of levels and compared the obtained data with those calculated from the experimental NLD data extracted by using the Oslo method (estimated data) as well as the predictions of different phenomenological and microscopic NLD models. The good agreement between our new cumulative curves with the estimated data allows us to deduce the values of the maximum excitation energy $E_{\rm max}$, which is defined as the energy threshold below which most of the excited levels have been observed, to be extended to around 1.2 and 1.8 MeV for the total and partial (spins of $[\frac{1}{2},\frac{3}{2}]\hbar$) NLD data, respectively. These values of $E_{\rm max}$ are higher than the corresponding values obtained by using the data presently existed in the ENSDF library. Moreover, the newly constructed cumulative curves also agree well with the recent microscopic exact pairing plus independent-particle model at finite temperature in which no fitting parameter has been employed.

All the results obtained within the present work are important as they will provide the updated information on the nuclear level structure and make a step forward to the completed level schemes of excited compound nuclei.

Acknowledgements.

N.N.A, N.X.H, P.D.K, H.H.T, N.Q.H acknowledge the support by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam through Grant No. 103.04-2017.323. They would also like to thank the Ministry of Science and Technology of Vietnam for the financial support through the project coded KC05.08/16-20. Sincerely thanks are given to Prof. Vuong Huu Tan (former Chairman of Vietnam Atomic Energy Institute) and Prof. Nguyen Nhi Dien (former Director of Dalat Nuclear Research Institute) for their important decisions and supports to implement the neutron beams at Dalat Nuclear Research Reactor, which have been continuously used for the nuclear structure study in Vietnam.