Deformed band structures in neutron-rich $^{152-158}$Pm isotopes

TL;DR

This study investigates high spin band structures in neutron-rich Pm isotopes using gamma-ray spectroscopy from fission experiments, revealing new excited states and exploring potential octupole deformations.

Contribution

It provides the first identification of excited states in certain Pm isotopes and extends the understanding of their rotational band structures at high spins.

Findings

Excited states in $^{157}$Pm and above isomers in $^{152,154,156,158}$Pm identified for the first time.

Rotational band structures extended to higher spins in odd-A Pm isotopes.

Octupole deformed shapes in neutron-rich Pm isotopes beyond N=90 are unlikely.

Abstract

High spin band structures of neutron-rich $^{152-158}$Pm isotopes have been obtained from the measurement of prompt $\gamma$-rays of isotopically identified fragments produced in fission of $^{238}$U+$^{9}$Be and detected using the VAMOS++ magnetic spectrometer and EXOGAM segmented Clover array at GANIL and also from the high statistics $\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$-$\gamma$ data from the spontaneous fission of $^{252}$Cf using Gammasphere. The excited states in $^{157}$Pm and those above the isomers in even-A Pm isotopes $^{152,154,156,158}$Pm have been identified for the first time. The spectroscopic information on the rotational band structures in odd-A Pm isotopes has been extended considerably to higher spins and the possibility of the presence of reflection asymmetric shapes is explored. The configuration assignments are based on the results of Cranked Relativistic Hartree-Bogoliubov calculations. From the systematics of bands in odd-A Pm isotopes and weak population of opposite parity bands, octupole deformed shapes in neutron rich Pm isotopes beyond $N=90$ seem unlikely to be present.

Tables

Table 1. Table 1: The energies (E γ ) and relative intensities (I γ ) of the γ 𝛾 \gamma rays assigned to different odd-A Pm isotopes along with the spin and parity of the initial ( J i π subscript superscript 𝐽 𝜋 𝑖 J^{\pi}_{i} ) and the final ( J f π subscript superscript 𝐽 𝜋 𝑓 J^{\pi}_{f} ) states and the energy of the initial state (E i ).

$E_{\gamma }{\left(keV\right)}^{}$111 $\gamma$-ray energy uncertainties are typically $\pm$ 0.2 keV, $\pm$ 0.5 keV and $\pm$ 1 keV around 200 keV, 500 keV and 1 MeV respectvely.	$E_i{\left(keV\right)}^{}$222 The maximum uncertainty of the level energy is upto 0.5%.	$J_i^{\pi }$	$\to$	$J_f^{\pi }$	$I_{\gamma }^{}(Err.)$333Intensities are normalized to 100 for 153,155Pm and to 10 for 157Pm. The errors quoted are the fitting errors.
153Pm
66	66	$7/2^{-}$	$\to$	$5/2^{-}$	24 (6)
85	151	$9/2^{-}$	$\to$	$7/2^{-}$	41 (11)
102	253	$\left(11/2^{-}\right)$	$\to$	$9/2^{-}$	74 (12)
112	311	$\left(11/2^{+}\right)$	$\to$	$\left(9/2^{+}\right)$	9 (5)
124	376	$\left(13/2^{-}\right)$	$\to$	$\left(11/2^{-}\right)$	100 (9)
133	199	$\left(9/2^{+}\right)$	$\to$	$7/2^{-}$	33 (6)
136	512	$\left(15/2^{-}\right)$	$\to$	$\left(13/2^{-}\right)$	98 (8)
151	151	$9/2^{-}$	$\to$	$5/2^{-}$	15 (8)
160	311	$\left(11/2^{+}\right)$	$\to$	$9/2^{-}$	36 (8)
165	678	$\left(17/2^{-}\right)$	$\to$	$\left(15/2^{-}\right)$	158 (9)444Combined intensity of 165 and 167 keV.
167	845	$\left(19/2^{-}\right)$	$\to$	$\left(17/2^{-}\right)$	-444Combined intensity of 165 and 167 keV.
178	430	$\left(13/2^{+}\right)$	$\to$	$\left(11/2^{-}\right)$	20 (6)
187	253	$\left(11/2^{-}\right)$	$\to$	$7/2^{-}$	30 (6)
192	1243	$\left(23/2^{-}\right)$	$\to$	$\left(21/2^{-}\right)$	80 (6)
206	1051	$\left(21/2^{-}\right)$	$\to$	$\left(19/2^{-}\right)$	71 (8)
212	1703	$\left(27/2^{-}\right)$	$\to$	$\left(25/2^{-}\right)$	59 (6)
226	376	$\left(13/2^{-}\right)$	$\to$	$9/2^{-}$	48 (11)
232	430	$\left(13/2^{+}\right)$	$\to$	$\left(9/2^{+}\right)$	14 (5)
248	1491	$\left(25/2^{-}\right)$	$\to$	$\left(23/2^{-}\right)$	45 (8)
260	512	$\left(15/2^{-}\right)$	$\to$	$\left(11/2^{-}\right)$	76 (9)
286	1989	$\left(29/2^{-}\right)$	$\to$	$\left(27/2^{-}\right)$	12 (3)
301	678	$\left(17/2^{-}\right)$	$\to$	$\left(13/2^{-}\right)$	92 (8)
332	845	$\left(19/2^{-}\right)$	$\to$	$\left(15/2^{-}\right)$	98 (9)
373	1051	$\left(21/2^{-}\right)$	$\to$	$\left(17/2^{-}\right)$	56 (8)
398	1243	$\left(23/2^{-}\right)$	$\to$	$\left(19/2^{-}\right)$	79 (11)
440	1491	$\left(25/2^{-}\right)$	$\to$	$\left(21/2^{-}\right)$	76 (12)
460	1703	$\left(27/2^{-}\right)$	$\to$	$\left(23/2^{-}\right)$	79 (9)
498	1989	$\left(29/2^{-}\right)$	$\to$	$\left(25/2^{-}\right)$	68 (12)
155Pm
67	67	$\left(7/2^{-}\right)$	$\to$	$5/2^{-}$	27 (8)
87	154	$\left(9/2^{-}\right)$	$\to$	$\left(7/2^{-}\right)$	54 (14)
105	259	$\left(11/2^{-}\right)$	$\to$	$\left(9/2^{-}\right)$	73 (5)
127	386	$\left(13/2^{-}\right)$	$\to$	$\left(11/2^{-}\right)$	100 (5)
142	528	$\left(15/2^{-}\right)$	$\to$	$\left(13/2^{-}\right)$	92 (5)
169	698	$\left(17/2^{-}\right)$	$\to$	$\left(15/2^{-}\right)$	81 (5)
174	872	$\left(19/2^{-}\right)$	$\to$	$\left(17/2^{-}\right)$	62 (5)
192	259	$\left(11/2^{-}\right)$	$\to$	$\left(7/2^{-}\right)$	27 (5)
202	1286	$\left(23/2^{-}\right)$	$\to$	$\left(21/2^{-}\right)$	24 (5)
213	1084	$\left(21/2^{-}\right)$	$\to$	$\left(19/2^{-}\right)$	41 (5)
223	1769	$\left(27/2^{-}\right)$	$\to$	$\left(25/2^{-}\right)$	27 (5)
232	387	$\left(13/2^{-}\right)$	$\to$	$\left(9/2^{-}\right)$	46 (5)
259	1546	$\left(25/2^{-}\right)$	$\to$	$\left(23/2^{-}\right)$	14 (3)
269	528	$\left(15/2^{-}\right)$	$\to$	$\left(11/2^{-}\right)$	51 (5)
311	698	$\left(17/2^{-}\right)$	$\to$	$\left(13/2^{-}\right)$	78 (8)
343	872	$\left(19/2^{-}\right)$	$\to$	$\left(15/2^{-}\right)$	70 (8)
387	1084	$\left(21/2^{-}\right)$	$\to$	$\left(17/2^{-}\right)$	46 (5)
415	1286	$\left(23/2^{-}\right)$	$\to$	$\left(19/2^{-}\right)$	38 (5)
461	1546	$\left(25/2^{-}\right)$	$\to$	$\left(21/2^{-}\right)$	38 (5)
482	1769	$\left(27/2^{-}\right)$	$\to$	$\left(23/2^{-}\right)$	41 (5)
157Pm
66	66	$\left(7/2^{-}\right)$	$\to$	$\left(5/2^{-}\right)$	2(1)
85	151	$\left(9/2^{-}\right)$	$\to$	$\left(7/2^{-}\right)$	5(2)
103	254	$\left(11/2^{-}\right)$	$\to$	$\left(9/2^{-}\right)$	6(1)
125	379	$\left(13/2^{-}\right)$	$\to$	$\left(11/2^{-}\right)$	9(1)
139	518	$\left(15/2^{-}\right)$	$\to$	$\left(13/2^{-}\right)$	6(2)
151	151	$\left(9/2^{-}\right)$	$\to$	$\left(5/2^{-}\right)$	-555Weak transition, intensity could not be determined.
165	683	$\left(17/2^{-}\right)$	$\to$	$\left(15/2^{-}\right)$	10(1)
172	855	$\left(19/2^{-}\right)$	$\to$	$\left(17/2^{-}\right)$	6(1)
188	254	$\left(11/2^{-}\right)$	$\to$	$\left(7/2^{-}\right)$	2(1)
201	1263	$\left(23/2^{-}\right)$	$\to$	$\left(21/2^{-}\right)$	4(1)
207	1062	$\left(21/2^{-}\right)$	$\to$	$\left(19/2^{-}\right)$	4(1)
228	379	$\left(13/2^{-}\right)$	$\to$	$\left(9/2^{-}\right)$	2(1)
252	1515	$\left(25/2^{-}\right)$	$\to$	$\left(23/2^{-}\right)$	2(1)
264	518	$\left(15/2^{-}\right)$	$\to$	$\left(11/2^{-}\right)$	7(2)
304	683	$\left(17/2^{-}\right)$	$\to$	$\left(13/2^{-}\right)$	6(1)
337	855	$\left(19/2^{-}\right)$	$\to$	$\left(15/2^{-}\right)$	6(1)
379	1062	$\left(21/2^{-}\right)$	$\to$	$\left(17/2^{-}\right)$	2(1)
408	1263	$\left(23/2^{-}\right)$	$\to$	$\left(19/2^{-}\right)$	3(1)
453	1515	$\left(25/2^{-}\right)$	$\to$	$\left(21/2^{-}\right)$	4(2)
476	1739	$\left(27/2^{-}\right)$	$\to$	$\left(23/2^{-}\right)$	7(4)

Table 2. Table 2: The energies (E γ ) and relative intensities (I γ ) of the γ 𝛾 \gamma  rays assigned to different even-A Pm isotopes along with the probable spin and parity of the initial ( J i π subscript superscript 𝐽 𝜋 𝑖 J^{\pi}_{i} ) and the final ( J f π subscript superscript 𝐽 𝜋 𝑓 J^{\pi}_{f} ) states and the energy of the initial state (E i ).

$E_{\gamma }{\left(keV\right)}^{}$111 $\gamma$-ray energy uncertainties are typically $\pm$ 0.2 keV, $\pm$ 0.5 keV and $\pm$ 1 keV around 200 keV, 500 keV and 1 MeV respectvely.	$E_i{\left(keV\right)}^{}$222 Level energies are given with respect to a level of energy x keV. The maximum uncertainty of the level energy is upto 0.5%.	$J_i^{\pi }$	$\to$	$J_f^{\pi }$	$I_{\gamma }^{}(Err.)$333Intensities are normalized to 100 for 152,154Pm and to 10 for 156Pm. The errors quoted are the fitting errors.
152Pm
76	76	$\left(I_0+1\right)$	$\to$	$\left(I_0\right)$	29 (8)
84	160	$\left(I_0+2\right)$	$\to$	$\left(I_0+1\right)$	31 (8)
92	251	$\left(I_0+3\right)$	$\to$	$\left(I_0+2\right)$	58 (13)
99	350	$\left(I_0+4\right)$	$\to$	$\left(I_0+3\right)$	100 (15)
112	462	$\left(I_0+5\right)$	$\to$	$\left(I_0+4\right)$	69 (6)
122	584	$\left(I_0+6\right)$	$\to$	$\left(I_0+5\right)$	44 (6)
126	710	$\left(I_0+7\right)$	$\to$	$\left(I_0+6\right)$	46 (6)
140	850	$\left(I_0+8\right)$	$\to$	$\left(I_0+7\right)$	29 (4)
158	1206	$\left(I_0+10\right)$	$\to$	$\left(I_0+9\right)$	19 (8)
160	160	$\left(I_0+2\right)$	$\to$	$\left(I_0\right)$	54 (10)
176	251	$\left(I_0+3\right)$	$\to$	$\left(I_0+1\right)$	25 (4)
191	350	$\left(I_0+4\right)$	$\to$	$\left(I_0+2\right)$	25 (4)
198	1048	$\left(I_0+9\right)$	$\to$	$\left(I_0+8\right)$	21 (4)
211	462	$\left(I_0+5\right)$	$\to$	$\left(I_0+3\right)$	31 (10)
234	584	$\left(I_0+6\right)$	$\to$	$\left(I_0+4\right)$	21 (6)
248	710	$\left(I_0+7\right)$	$\to$	$\left(I_0+5\right)$	23 (6)
266	850	$\left(I_0+8\right)$	$\to$	$\left(I_0+6\right)$	40 (6)
338	1048	$\left(I_0+9\right)$	$\to$	$\left(I_0+7\right)$	38 (10)
356	1206	$\left(I_0+10\right)$	$\to$	$\left(I_0+8\right)$	31 (10)
154Pm
94	94	$\left(I_0+1\right)$	$\to$	$\left(I_0\right)$	43 (11)
109	203	$\left(I_0+2\right)$	$\to$	$\left(I_0+1\right)$	43 (6)
126	329	$\left(I_0+3\right)$	$\to$	$\left(I_0+2\right)$	46 (9)
141	470	$\left(I_0+4\right)$	$\to$	$\left(I_0+3\right)$	71 (6)
158	628	$\left(I_0+5\right)$	$\to$	$\left(I_0+4\right)$	20 (6)
174	802	$\left(I_0+6\right)$	$\to$	$\left(I_0+5\right)$	29 (11)
189	991	$\left(I_0+7\right)$	$\to$	$\left(I_0+6\right)$	17 (6)
203	203	$\left(I_0+2\right)$	$\to$	$\left(I_0\right)$	40 (6)
235	329	$\left(I_0+3\right)$	$\to$	$\left(I_0+1\right)$	100 (11)
267	470	$\left(I_0+4\right)$	$\to$	$\left(I_0+2\right)$	83 (9)
299	628	$\left(I_0+5\right)$	$\to$	$\left(I_0+3\right)$	97 (9)
331	802	$\left(I_0+6\right)$	$\to$	$\left(I_0+4\right)$	69 (9)
363	991	$\left(I_0+7\right)$	$\to$	$\left(I_0+5\right)$	63 (9)
397	1199	$\left(I_0+8\right)$	$\to$	$\left(I_0+6\right)$	57 (9)
425	1416	$\left(I_0+9\right)$	$\to$	$\left(I_0+7\right)$	69 (9)
464	1663	$\left(I_0+10\right)$	$\to$	$\left(I_0+8\right)$	51 (11)
483	1899	$\left(I_0+11\right)$	$\to$	$\left(I_0+9\right)$	74 (11)
156Pm
90	90	$\left(I_0+1\right)$	$\to$	$\left(I_0\right)$	7 (3)
103	370	$\left(I_0+4\right)$	$\to$	$\left(I_0+3\right)$	9 (3)
108	198	$\left(I_0+2\right)$	$\to$	$\left(I_0+1\right)$	10 (1)
119	489	$\left(I_0+5\right)$	$\to$	$\left(I_0+4\right)$	6 (1)
135	624	$\left(I_0+6\right)$	$\to$	$\left(I_0+5\right)$	4 (1)
151	775	$\left(I_0+7\right)$	$\to$	$\left(I_0+6\right)$	-444Weak transition, intensity could not be determined.
172	370	$\left(I_0+4\right)$	$\to$	$\left(I_0+2\right)$	10 (1)
198	198	$\left(I_0+2\right)$	$\to$	$\left(I_0\right)$	6 (1)
222	489	$\left(I_0+5\right)$	$\to$	$\left(I_0+3\right)$	7 (1)
236	326	$\left(I_0+3\right)$	$\to$	$\left(I_0+1\right)$	6 (1)
254	624	$\left(I_0+6\right)$	$\to$	$\left(I_0+4\right)$	9 (1)
271	469	$\left(I_0+4\right)$	$\to$	$\left(I_0+2\right)$	9 (3)
286	775	$\left(I_0+7\right)$	$\to$	$\left(I_0+5\right)$	9 (1)
307	633	$\left(I_0+5\right)$	$\to$	$\left(I_0+3\right)$	7 (1)
319	943	$\left(I_0+8\right)$	$\to$	$\left(I_0+6\right)$	10 (1)
341	810	$\left(I_0+6\right)$	$\to$	$\left(I_0+4\right)$	6 (1)
350	1125	$\left(I_0+9\right)$	$\to$	$\left(I_0+7\right)$	10 (4)
376	1009	$\left(I_0+7\right)$	$\to$	$\left(I_0+5\right)$	6 (1)
384	1327	$\left(I_0+10\right)$	$\to$	$\left(I_0+8\right)$	7 (1)
414	1539	$\left(I_0+11\right)$	$\to$	$\left(I_0+9\right)$	10 (4)
443	1452	$\left(I_0+9\right)$	$\to$	$\left(I_0+7\right)$	3 (1)
451	1778	$\left(I_0+12\right)$	$\to$	$\left(I_0+10\right)$	6 (1)
475	2014	$\left(I_0+13\right)$	$\to$	$\left(I_0+11\right)$	9 (1)

Full text

I Introduction

The many-body correlations in atomic nuclei can lead to various shapes other than those which are spherically symmetric. These include reflection symmetric prolate or oblate shapes having quadrupole deformation, triaxial shapes having both quadrupole deformation and axial asymmetry and reflection asymmetric “pear shape” with static octupole deformation. The nuclei of rare earth region with $N=88-90$ are well known to have transitional character: from nearly spherical or weakly deformed shapes for $N<88$ to well deformed shapes for $N>90$. A deformed region beyond $N=90$ is known from the systematics of the first excited states of even-even nuclei around $Z=55-66$ Casten . The nuclei in the $A=140-150$ mass region are expected to have octupole collectivity. This is because their Fermi levels lie between the $f_{7/2}$ and $i_{13/2}$ neutron orbitals and between the $d_{5/2}$ and $h_{11/2}$ proton orbitals, which differ by $\Delta j=\Delta l=3$; this leads to an increase of octupole correlations  Ahmad ; Butler . The first experimental signature of octupole collectivity in this region was reported for neutron rich Ba isotopes Leander85 ; Phillips and later on more definitively established in neutron-rich odd and even A Ba and Ce nuclei Zhu95 ; Zhu99 ; Chen06 ; Brewer and other rare earth nuclei Sheline . Direct evidence of static octupole deformation in neutron rich nucleus 144Ba has been reported recently Bucher .

There are several experimental fingerprints of static octupole deformation in nuclei which are discussed in details in Refs. Ahmad ; Butler ; Afana95 . One of them is the presence of specific features of rotational bands. Alternating parity bands with positive and negative parity states forming the sequence $I^{+}$, $(I+1)^{-}$, $(I+2)^{+}$ … appear in even-even nuclei Butler . Parity doublet bands are formed in odd and odd-odd nuclei. In these bands, parity doubling leads to the appearance of the pair of the states with spin $I$ but opposite parities Butler . Note that a parity doublet band can be represented as a pair of alternating parity bands with simplexes $s=+i$ and $s=-i$ Butler . The opposite parity states of given simplex in parity doublet bands are typically connected by strong E1 transitions, which is another possible experimental signature of reflection asymmetric shape. However, the electric dipole moment is built from delicate balance of proton and neutron contributions Butler1 . As a result, low B(E1) rates do not necessarily exclude static octupole deformation and vice versa. For example, the large B(E1) strengths in $N=92$ isotones 155Eu and 157Tb could also be explained without considering static octupole deformation Hartley . The behavior of alternating-parity and parity doublet bands with spin offers another clue on the presence of static octupole deformation since the rotation could stabilize the octupole deformation Naz92 ; Butler1 ; Ana1993 . Therefore, to understand the evolution of nuclear shape and nature of deformation of nuclei in this region, it is important to have more experimental data on high spin states with increasing neutron number.

The observation of the bands with features typical for parity doublet bands in odd-A and odd-odd nuclei in this region has also lead to various theoretical efforts to interpret these results in terms of static octupole deformation Leander84 ; Afana95 . Shell correction methods based on reflection asymmetric Woods-Saxon model were also used to explain the experimental observation of local quenching in E1 strength in some of the cases Butler1 .

The heavier isotopes of rare earth region, which are mostly neutron-rich, can be accessed by the fission process. The spectroscopy of heavy fission fragments provides the opportunity to investigate deformation effects as a function of neutron number for a particular isotope chain. Pm nuclei, with a wide isotopic range, are good candidates to explore the evolution of deformation with neutron number and possible role of octupole deformation in this region. It may be noted that there are no stable isotopes of Pm and that the isotopes beyond 151Pm are known only through radioactive decay studies William ; Shibata ; Taniguchi ; Karlewski ; Greenwood ; MShibata , proton transfer measurements Burke ; Lee and spontaneous fission of 252Cf source Hwang . This is mainly due to non-availability of suitable target-projectile combination to produce the nuclei in fusion evaporation reaction with large cross section. The high spin states of neutron rich nuclei in this mass region can be efficiently produced in fission. Isotopic identification of nuclei is critical to carry out spectroscopy of these exotic nuclei. Usually the technique of high fold $\gamma-\gamma$ coincidences and the cross coincidence relationships among the heavy and light fragment partners of the fission process are utilised to assign the $\gamma$ rays to a particular isotope. But in the case of extreme neutron rich isotopes, for which not a single $\gamma$ transition is known, it is very difficult to assign the $\gamma$ rays to the level scheme of a particular isotope on the basis of only $\gamma-\gamma$ coincidence. Furthermore, the presence of low-lying long-lived isomers in certain nuclei hinders the prompt coincidence between $\gamma$-rays below and above the isomer. In such cases, even if some of the transitions below the isomer are known, the band structure above the isomer cannot be obtained by using high fold $\gamma$ coincidence techniques. Thus, a direct isotopic (A,Z) identification of nuclei is essential for an unambiguous assignment of $\gamma$ rays. The high spin experimental data on neutron rich Pm isotopes was very limited prior this study. In fact, no in-beam high spin spectroscopic measurements are available beyond 151Pm.

The bands with features typical for parity doublet bands extending to high spins have been found in odd-A Pm isotopes for $N=86$ 147Pm 147pm , $N=88$ 149Pm Jones and $N=90$ 151Pm Vermeer ; Urban . The possibility of the presence of a reflection asymmetric shape at $N=92$ has also been reported from the observation of enhanced E1 transitions between a couple of low lying states of an band structure (which has typical features of parity doublet bands) in 153Pm measured in $\beta$-decay Taniguchi . Although the band structures observed in 151Pm and 153Pm are very similar, the origin of the ground state band in these two nuclei are quite different. In 151Pm the band head of the ground band is 5/2+ based on the [413]5/2+ configuration, originating from the $g_{7/2}$ orbital, whereas, the ground band in 153Pm with larger prolate deformation is based on the configuration [523]5/2-, originating from the high-j $h_{11/2}$ orbital. The rotational band based on the $\pi$5/2[532] state has also been identified in 155Pm from the spontaneous fission of 252Cf source Hwang , whereas no excited states in 157Pm are reported so far. Recently, $\mu$s isomers are observed in 158,159,161Pm, produced by in flight fission of 238U beam Yoko . Few lower spin members of the rotational band in 159,161Pm have also been observed in this study of delayed $\gamma$ ray spectroscopy of $\mu$s isomers. It would be interesting to extend the level structure of neutron-rich Pm isotopes to higher spins to understand the deformation effects as a function of N/Z and explore which kind of nuclear shapes (reflection symmetric quadrupole deformed or reflection asymmetric octupole deformed) exist at higher N/Z ratios.

For the neutron-rich odd-odd Pm isotopes, the information about the excited states is rather scarce, mainly because of the presence of long lived low lying isomers. Even the excitation energies of the long lived isomers are not well determined in most of the cases. The spectroscopic information on the odd-odd neutron-rich Pm isotopes above $N=90$ are reported from $\beta$-decay or decay of isomeric transition studies William ; Shibata ; Karlewski ; Greenwood ; Dauria ; MShibata . Thus, the information about the structure of the states above the long lived isomers of these odd-odd Pm isotopes can only be obtained by directly populating the high spin states via in-beam prompt spectroscopy. In the presence of a long lived isomer, even if some of the $\gamma$-rays below the high spin isomer are known, the assignment of $\gamma$-rays above the isomer of a particular isotope is challenging, as $\gamma$-$\gamma$ coincidences across a long lived isomeric state are difficult. A few low-spin states in 152Pm are known from $\beta$-decay of 152Nd William ; Shibata and the existence of two high spin isomers (7.5 min (4*±) and 18 min ($\geq$ 6+)) have also been identified from these studies. The excited states of 154Pm have been identified from the $\beta$-decay of 154Nd Karlewski ; Greenwood and the existence of two isomeric levels of 2.8 min and 1.8 min with probable spin assignment of J$\leq$3 were reported in Ref. Dauria from the observed $\beta$-decay and associated log-ft values corresponding to the $\beta$-decay of these isomeric states to 154Sm. For 156Pm, an isomeric state at 150.3 keV (with a tentative Jπ* of 1-) was identified and found to de-excite to the ground state by a M3 transition MShibata . In Ref. Hwang the $\gamma$ rays from the high spin states of 156Pm were reported, but, as discussed later in this manuscript, those $\gamma$ rays actually belong to 157Pm. No spectroscopic information above these isomeric states in 152,154,156Pm are known prior to the present work. In the case of 158Pm, the evidence of the existence of a $\mu$s isomer and the isomeric transition decay from that state has recently been reported Yoko . No other excited states of 158Pm are known prior to the present study.

In the present work, the $\gamma$ rays are detected with EXOGAM Sim00 segmented Clover detectors, in coincidence with the detected fission fragment at the focal plane of VAMOS++ spectrometer Rej11 with isotopic (A,Z) identification. Thus, the assignment of $\gamma$ rays to a particular isotope is unambiguous. Once the identification of $\gamma$-ray is ensured, the details of the level scheme at higher spin can be obtained from the high-fold $\gamma$ coincidence data from 252Cf fission using Gammasphere. In the present work the prompt $\gamma$ rays of neutron-rich Pm isotopes have been reported up to $N=97$ and the results are interpreted in terms of rotational band structures. The in-beam populations of the prompt transitions of 153Pm is reported for the first time and the level scheme has been extended considerably to higher spins upto (29/2-). The rotational band of 155Pm has also been extended to higher spins compared to previous work Hwang . The transitions of 157Pm are reported for the first time in this paper. Some of these transitions were assigned to 156Pm in Ref. Hwang from the measurement of spontaneous fission of 252Cf. For the odd-odd Pm isotopes, the first in-beam prompt spectroscopy measurements of 152-158Pm are reported from the present work. The band structures above the high spin isomers in these nuclei have been identified for the first time. The results are discussed from the systematics of band properties. The Cranked Relativistic Hartree-Bogoliubov calculations are also performed to understand configuration assignments.

The paper is organized as follows. Section II describes the details of experiment and the analysis of experimental data. Obtained results and the level schemes for odd-A and even-A Pm nuclei are presented in Sec. III. The discussion of the observables of interest and the interpretation of physical situation are carried out in Section IV. Finally, Sec. V summarizes the results of our work.

II Experiment

The measurements were carried out by using two complementary methods, namely (i) by direct identification of the fission fragments (A,Z) at the focal plane of the large acceptance magnetic spectrometer VAMOS++ and detection of corresponding in-beam $\gamma$ rays in coincidence and (ii) by detection of high fold $\gamma$ coincidence data from 252Cf spontaneous fission. The first method improves the selectivity and sensitivity of the measurements by unambiguous identification of the particular isotopes and the second one facilitates the study of high spin level structure using high-fold $\gamma$ coincidence techniques. The power of combining the two sets of data has been demonstrated earlier in case of study of neutron-rich Pr isotopes Wang .

The measurements of (A,Z) identification of the fission fragments and fragment-$\gamma$ coincidence were carried out at Grand Accelerateur National d’Ions Lourds (GANIL) using a 238U beam at 6.2 MeV/u ($\sim$0.2 pnA) on a 10-micron thick 9Be target. The fission fragments were directly identified by mass number (A), atomic number (Z) in the VAMOS++ magnetic spectrometer Rej11 placed at $20^{\circ}$ with respect to the beam axis. The elemental identification (Z) of the fission fragments were obtained from energy loss ($\Delta$E) in the isonization chamber and the total energy (E) measured by the Si detectors, placed at the focal plane of VAMOS++ spectrometer. The Time-Of-Flight (TOF) was measured between the two Multi-Wire Parallel Plate Avalanche Counters (MWPPAC), one placed just after the target and another at the focal plane. The (x,y) postions of the detected fragments were determined by the two Drift chambers at the focal plane. The various measured positions, energies and times along with the known magnetic field were used to determine, on an event-by-event basis, the mass (M), charge state ($Q$), Z, and the velocity vector ($\vec{\rm{v}}$) for the detected fragment Rej11 . The magnetic rigidity (B$\rho$) was obtained by applying a reconstruction procedure. The parameters (M/Q) and (M) were obtained independently using the reconstructed magnetic rigidity and from the measured velocity and total energy. A two-dimensional spectrum of Q an M/Q provides a clean and unambiguous identification of various isotopes detected at the focal plane. Fig. 1 shows the identification plot of Q vs M/Q after selection of $Z=61$. The prompt $\gamma$ rays were measured in coincidence with the isotopically-identified fragments, using the EXOGAM array Sim00 , consisted of 11 Compton-suppressed segmented Clover HPGe detectors placed at 15 cm from the target position. The $\gamma$-ray energies of the fragments were obtained event by event after Doppler correction from the measured $\vec{\rm{v}}$ using the VAMOS++ spectrometer and with the known angle of the segment of the relevant clover detector Rej11 ; Sam08 . More details of the setup and the measurements at GANIL can be found in Refs. Na14 ; Na14a .

The high fold $\gamma$ coincidence data were obtained from the measurements of 252Cf spontaneous fission at the Lawrence Berkeley National Laboratory (LBNL) using 101 HPGe detectors of Gammasphere. A 62-$\mu$Ci 252Cf source was sandwiched between two Fe foils of thickness 10 mg/cm2. The data were sorted into $\gamma$-$\gamma$-$\gamma$ and higher fold $\gamma$ events to form 3D cube and 4D cubes and were analyzed using the RADWARE package Rad . More details of this experiment and analysis procedures can be found in 150Ce ; 105Nb .

III Results

III.1 Odd-A Pm isotopes

Doppler corrected $\gamma$-ray spectra of odd-A Pm isotopes, detected in the present work by EXOGAM segmented Clover detectors, after the (A,Z) selection of the respective isotopes at the focal plane of VAMOS++ spectrometer, are shown in Fig. 2. All the transitions of 151Pm up to spin 27/2 $\hbar$, observed in the present work confirm those previously reported Urban ; Vermeer . The corresponding spectrum is shown in Fig. 2(a) to highlight the quality of data. For neutron rich odd-A Pm isotopes, transitions known from previous $\beta$-decay studies, are labelled. Some of the $\gamma$-rays (as shown in Fig. 2), though identified as belonging to the corresponding odd-A Pm isotopes through (A,Z) gating, could not be placed in the respective level schemes due to insufficient $\gamma$-$\gamma$ coincidence information. The $\gamma$ rays of 153,157Pm from in-beam prompt spectroscopy are being reported for the first time here and new level schemes are proposed. New transitions in 155Pm have also been identified and the level scheme has been extended to higher spins compared to that previously reported Hwang . The $\gamma$ rays, assigned to various odd-A Pm isotopes, along with their relative intensities and the level energies, obtained from the (A,Z) gated spectra are shown in Table. LABEL:tab:Table1. The quoted errors are the fitting errors. The probable spin-parity assignments of the initial and final states of the transitions have been obtained using the known systematics of odd-A Pm isotopes. The statistics was not enough to carry out any angular distribution or polarization measuremets for such neutron rich nuclei.

Information on the excited states of 153Pm was known from (t,$\alpha$) and (d, 3He) transfer reactions  Burke ; Lee . The levels pertaining to the bands based on Nilsson orbitals 5/2-[532], 5/2+[413], 3/2+[411] were identified from the measured particle angular distributions, without detection of any decaying $\gamma$ transitions between the states. First indication of band structure in 153Pm, which has typical features of parity doublet bands, was reported from $\beta$-decay measurements Taniguchi . In the present work the first information on the high spin states in 153Pm is obtained, which is extended up to 1989 keV (29/2-) from in-beam prompt $\gamma$ spectroscopy measurements. The $\gamma$ spectrum in coincidence with the 153Pm fragments identified using the VAMOS++ spectrometer is shown in Fig. 2 (b). The $\gamma$ spectra corresponding to the gates of 102, 136 and 165 keV transitions are shown in Fig. 3, obtained from the $\gamma$-$\gamma$ matrix after selection of 153Pm fragment from 238U+9Be-induced fission data. The mutual coincidence of 102, 124, 136, 165, 167 keV $\gamma$ rays can be clearly seen from the coincidence spectra shown in Fig. 3(a-c). The presence of doublet 165-167 keV could be confirmed from the $\gamma$-$\gamma$ coincidence, as it is evident from Fig. 3(c) corresponding to the coincidence spectrum of 165 keV transition. The presence of other transitions decaying from higher excited states of 153Pm, is also visible from the coincidence spectra of Fig. 3(a-c). The triple coincidence spectra by gating on the 39 keV Pm-X-rays and other strong transitions of 102, 124 and 136 keV are shown in Fig. 4. The presence of cascade $\gamma$ rays in the 5/2- ground band of 153Pm is clearly visible from these spectra. The level scheme of 153Pm, as shown in Fig. 5, has been obtained on the basis of energy systematics of known odd-A Pm isotopes, the $\gamma$-$\gamma$ coincidence measurements and intensity balance. The placement of the crossover transitions are also made from the energy-sum systematics. The spin-parity of the 7/2-, 9/2- states are adopted from a previous work on $\beta$-decay Taniguchi . In the present work, the data statistics for each detector angle was insufficient to carry out an angular distribution analysis. Therefore, the spin-parities of the other excited levels are only tentatively assigned from the systematics of odd-A Pm isotopes. The observed intensities of transitions placed in the level scheme of 153Pm and the corresponding excited levels with tentative spin-parity assignments are given in Table. LABEL:tab:Table1. It may be noted that, the low energy dipole transitions can be significantly converted and contain a mixing of higher order multipoles. As mixing ratios (from angular distributions) of the transitions or the conversion electrons could not be measured in the present experiment, therefore, only the observed $\gamma$ ray intensities are shown in Table. LABEL:tab:Table1. The intensity mismatch for some of the lower lying states (7/2-, 9/2- and 11/2-) can be due to the fact that the low energy dipole transitions are not pure and depending on the mixing ratios the conversion coefficients will be altered.

The presence of a parity doublet band in 153Pm was indicated earlier in Ref. Taniguchi . The transitions pertaining to this band, as reported in Ref. Taniguchi , could also be confirmed from the present data. From the present measurement, the 112 keV $\gamma$ ray has been placed in this band as the transition from (11/2+) to (9/2+) level. Also, the 178 keV and 232 keV $\gamma$ rays have been tentatively placed in this band, as these two transitions could not be observed in coincidence with any of the strong transitions of the band based on (5/2-) state. Though $\gamma$-$\gamma$ coincidence information could not be obtained for these transitions due to limited statistics, their presence in 153Pm is confirmed, as the $\gamma$-spectra in the present work have been obtained after (A,Z) identification.

The spectroscopic information on the excited states of 155Pm and the associated $\gamma$ rays were first known from the study of the $\beta$-decay of 155Nd Greenwood1 . Later, the existence of a rotational band extending up to (23/2-) in 155Pm was reported  Hwang from the measurements of 252Cf fission. This band has been extended up to (27/2-) in the present measurements. The $\gamma$-ray singles spectrum, as obtained using EXOGAM Clover array, in coincidence with detected 155Pm at the focal plane of VAMOS++ spectrometer is shown in Fig. 2(c). The new transitions as compared to earlier reported Hwang are observed from this spectrum. The $\gamma$ spectra corresponding to the gates of 105, 127 and 142 keV transitions are shown in Fig. 6, obtained from the $\gamma$-$\gamma$ matrix after selection of 155Pm fragment from 238U+9Be-induced fission data. The placement of 105, 127 and 142 keV $\gamma$ rays in coincidence with each other and the higher lying transitions are supported from the coincidence spectra shown in Fig. 6 (a - c). Coincidence of the transitions are checked using various gating conditions and also from different added gates. A coincidence spectrum corresponding to double gates of 39 keV (Pm X-ray) and 127 keV, obtained from 252Cf data, is shown in Fig. 7. In this coincidence spectrum, the 159 and 217 keV peaks appear due to the presence of 126-159-218-217 cascade in 103Nb and its partner La Kβ X-ray at 38 keV, which is present as a contamination in 155Pm. The 217 peak could also come from 94Rb fission partner in this case. The energy sum, intensities and the coincidence information of the observed $\gamma$ rays are used to obtain the level scheme, as shown in Fig. 8. The spin-parities indicated in Fig. 8 are only tentative, as angular distribution and polarization measurements were not possible from the present data. Also, it may be noted that no indication of any side band could be found for 155Pm from the present data.

The excited states of 157Pm are identified for the first time from the present measurements. Some of the transitions were earlier assigned to 156Pm Hwang . The incorrect placement was mainly due to problem of identification only from the high fold $\gamma$ coincidence data for such exotic nuclei with a small production cross section. In the present work, the particular fragment is directly isotopically identified using the VAMOS++ spectrometer and the corresponding Doppler corrected $\gamma$-rays are detected by EXOGAM segmented Clover array, leading to an unambiguous identification of the relevant transitions. The $\gamma$-ray singles spectrum in coincidence with detected 157Pm fragments is shown in Fig. 2(d). The $\gamma$-$\gamma$ coincidences for such neutron-rich nucleus were not possible from the measurements of 238U+9Be reaction, but were obtained from 252Cf fission data of Gammasphere array. The two representative coincidence spectra corresponding to double gates of 39 keV (Pm X-ray) and 264 keV, 39 keV (Pm X-ray) and 103 keV are shown in Fig. 9. The proposed level scheme of 157Pm, obtained from the present work, is shown in Fig. 10. Only transitions seen in Fig. 2(d) and in multiple coincidence gates such as in Fig. 9, are placed in Fig. 10. An indication of the transitions 151 keV and 188 keV could be observed in (A,Z) gated spectra. These transitions are tentatively placed as the E2 crossover transitions corresponding to (9/2-) to (5/2-) and (11/2-)to (7/2-) states respectively. The level scheme is obtained mainly from the energy level systematics of the neighbouring isotopes, energy-sum, intensity balance and coincidence information. For certain levels (11/2- state) the observed $\gamma$ ray intensities feeding in and decaying out of the level are imbalanced. This can be accounted by considering the proper conversion of lower energy dipole $\gamma$ rays according to their mixing with higher order multipoles. Spin-parity of the states are only tentatively assigned from the systematics of odd-A Pm isotopes of lower masses.

III.2 Odd-odd Pm isotopes

For odd-odd Pm isotopes, the present work reports the first in-beam measurements of prompt $\gamma$ rays of neutron-rich 152,154,156,158Pm isotopes. The Doppler corrected $\gamma$-ray spectra of odd-odd Pm isotopes, detected in the present work in coincidence with the respective isotopes identified at the focal plane of VAMOS++ spectrometer are shown in Fig. 11. The $\gamma$ rays which could not be placed in the level schemes of respective even-A Pm isotopes due to lack of $\gamma$-$\gamma$ coincidence information, are labelled in Fig. 11 (see caption of Fig. 11). However, the identification of these transitions to the corresponding even-A Pm isotopes are confirmed from (A,Z) gating condition. All these neutron-rich odd-odd Pm isotopes are known to have long-lived isomers and the information on excited states of these isotopes were extracted only from $\beta$-decays. Prior to this study, the information on the high spin states of these neutron rich nuclei were not available. This is because these states are difficult to populate in reactions other than fission and unambiguous assignment of the $\gamma$ transitions of such neutron rich nuclei cannot be made without direct identification of the corresponding isotope in coincidence. In particular, the presence of long-lived isomers make the situation more complicated, as correlation of the transitions below and above the isomer is not possible only from prompt $\gamma$-$\gamma$ coincidence without any isotopic identification. In the present work, only the prompt in-beam $\gamma$-rays are detected with isotopic identification as the experimental setup was not optimized to detect the delayed $\gamma$-rays. The $\gamma$ rays, assigned to various even-A Pm isotopes, along with their relative intensities, obtained from the (A,Z) gated spectra are shown in Table. LABEL:tab:Table2. The probable spin-parity the initial and final states are only tentatively assigned from the systematics of even-A Pm isotopes. The level energies given in Table. LABEL:tab:Table2 are with respect to a reference level and the quoted errors are the fitting errors. The $\gamma$ rays observed and the proposed level schemes of particular cases are discussed below.

The precise measurement of the low spin levels of 152Pm were established from the decay of mass separated 152Nd Shibata . Strong $\beta$ decay feeding to the ground state (1+) and other low spin states (mostly 1+) of 152Pm are reported. The presence of two long-lived isomers with half lives 7.5 min and $\approx$18 min were identified in 152Pm and the most probable spin-parity for these isomeric states were proposed to be of 4*±* and $\geq$6+, respectively, based on the decay feeding to 152Sm levels William . Though the total $\beta$-decay energy of 7.5 min isomer was found to be 3.6 $\pm$ 0.1 MeV, the excitation energy of the proposed $\approx$18 min isomer could not be established. In the present work the prompt $\gamma$ ray spectrum obtained in coincidence with 152Pm fragments is shown in Fig. 11(a). The information about the coincidence relationships of these $\gamma$ rays have been obtained from the limited statistics of $\gamma$-$\gamma$ coincidence from 238U+9Be reaction. The coincidence spectrum corresponding to the sum of gates of 112 and 140 keV $\gamma$ rays is shown in Fig. 12. The presence of 92-99-112-140-158-198 keV cascade can be seen from this spectrum. The (A,Z) gated $\gamma$ rays of 152Pm (Fig. 11(a)) are then used to obtain the coincidence information from the high-fold $\gamma$-$\gamma$-$\gamma$ 3D cube and $\gamma$-$\gamma$-$\gamma$-$\gamma$ 4D cubes from the Gammasphere data. A representative spectrum corresponding to triple gate of 92-99-112 keV cascade is shown in Fig. 13. The level scheme, as shown in Fig. 14, is obtained from the $\gamma$-$\gamma$ coincidence information and the energy-sum systematics. As none of the $\gamma$-rays, reported earlier from the $\beta$-decay of 152Nd Shibata are observed in the present work, the excitation energy of the lowest level of 152Pm from the current work cannot be established. As mentioned earlier, mainly high spin states are populated in fission reactions. As a result, the excited states of 152Pm populated in the present work most probably decay to either of the known high spin isomeric states. Thus, the excitation energy and spin of the lowest level of the proposed scheme as (0+x) and I0 respectively.

For 154Pm, the $\gamma$ ray spectrum in coincidence with 154Pm fragments detected from 238U+9Be reaction, is shown in Fig. 11(b). The coincidence spectrum corresponding to some of the gates of 109, 126 and 141 keV $\gamma$ rays are shown in Fig. 15. The spectra corresponding to the triple gates obtained from the high fold $\gamma$ coincidence data on spontaneous fission of 252Cf at Gammasphere are shown in Fig. 16. The level scheme of 154Pm proposed in the present work is shown in Fig. 17. It can be seen from the $\gamma$ spectrum of Fig. 11(b) that several $\gamma$ rays, such as, 99, 115, 133, 165, 179, 214, 248, 311, 344 keV, identified as belonging to 154Pm, are not placed in the proposed level scheme. It is possible that these unassigned $\gamma$ rays belong to a different band in 154Pm. Though the excitation energy of the 2.68 min isomer (3, 4) is not known experimentally, this state is considered as the probable ground state from the consideration of $\beta$ transition rates and expected two quasi-particle configuration  Sood1990 compared to the other 1.73 min isomer of proposed spin (0-, 1-). Thus, in the case of 154Pm, the proposed level scheme can most probably be built on the 2.68 min (3, 4) state. But, as the energy of the 2.68 min (3, 4) state is not established experimentally, the lowest level of the proposed scheme of Fig. 17 is marked as (0+x), I0.

The $\gamma$ ray spectrum of 156Pm obtained in the present work from 238U+9Be reaction, in coincidence with 156Pm fragments identified in the focal plane of VAMOS++ spectrometer is shown in Fig. 11(c). It may be noted that none of the $\gamma$ rays assigned to 156Pm, from the previous study of spontaneous fission of 252Cf by Hwang et al. Hwang , could be observed in this spectrum. These $\gamma$ rays are now assigned to 157Pm in the present work, as described in Section III-A. Thus the unique identification of $\gamma$ rays in case of such an exotic nucleus was difficult from 252Cf spontaneous fission measurements, where the high-fold $\gamma$ coincidences and the cross coincidence relationship among the fission fragment partners are utilized to assign the $\gamma$ rays to a particular nucleus. In the present work, as the fragments are directly identified at the focal plane of the spectrometer by (A,Z) tagging, the corresponding coincident $\gamma$ rays are uniquely assigned to that particular fragment. Within the limited statistics of (A,Z) gated data from 238U+9Be reaction, no $\gamma$-$\gamma$ coincidence information could be obtained. However, the coincidence relationship among various $\gamma$ rays identified in (A,Z) gated spectrum could be obtained from the high-fold data from the spontaneous fission of 252Cf, measured using Gammasphere array. The coincidence spectra corresponding to the triple gates of $\gamma$ transitions of 156Pm are shown in Fig. 18. It may be noted that in these coincidence spectra from 252Cf fission data, the $\gamma$ rays of the corresponding fission partner can also be present in coincidence, as there is no (A,Z) selection in this case. The 142 keV strong transition observed in each coincidence spectra of Fig. 18, is actually from the fission partner 92Rb. The level scheme, shown in Fig. 19, is obtained from the coincidence relationship among various $\gamma$ rays cascades. The low energy transition of 68 keV is tentatively placed, as the transitions placed above and below the 68 keV are found to be in coincidence. Shibata et. al. MShibata earlier reported $\gamma$ rays from the $\beta$-decay of 156Nd and did not propose any level scheme, except for the the isomeric transition decay. It is possible that the present level scheme of 156Pm is built on the ground state, which is proposed to be of higher spin (J=4) compared to the known isomeric state at 150.3 keV. A ground state of 4*(-)* was proposed in Ref. MShibata , with the observation of a M3 transition from the (1-) isomer. However, in Ref. NDS113 , the most probable ground state is adopted to be a 4*(+)* and the isomer as (1+). From the discussion of Refs. MShibata and  NDS113 , it appears that configurations corresponding to both 4*(+)* and 4*(-)* can be present in this region. Though some of the $\gamma$ rays reported in Ref. MShibata are found to have energies close to those assigned to 156Pm in the present work, it cannot be firmly concluded that the corresponding excited states populated from $\beta$ decay of 156Nd are the same as that observed from the present work. Thus the possibility of placing the present level scheme to a state above the ground state cannot be ruled out. In view of above possibilities, we prefer to keep the lowest state of the proposed scheme as (0+x, I0).

The $\gamma$ rays from the excited states of 158Pm are identified for the first time in the present work and the corresponding spectrum is shown in Fig. 11(d). Seven new $\gamma$ rays have been identified as belonging to 158Pm from data of 238U+9Be reaction. However, for 158Pm, no level scheme could be obtained, as the statistics is very limited.

IV Discussion

The nuclei under study are located at the boundary of octupole deformed lanthanide region (see Refs. Butler ; Agb16 ). If located in the vicinity of the respective Fermi levels, the deformed orbitals emerging from the proton $d_{5/2}$ and $h_{11/2}$ spherical subshells and from neutron $f_{7/2}$ and $i_{13/2}$ spherical subshells are responsible for possible occurrence of reflection asymmetric shapes. These spherical subshells satisfy the $\Delta j=\Delta l=3$ condition which leads to an increase of octupole correlations. The predictions of model calculations for the position of this boundary depend on the underlying mean field and its parametrization (see discussion in Sec. IV of Ref. Agb16 ). For example, the highest neutron number for which covariant density functional calculations predict octupole deformation in the ground states of even-even Nd ($Z=60$) nuclei is $N=90$ for most of covariant energy density functionals. On the contrary, microscopic+macroscopic calculations and Hartree-Fock calculations with finite range Gogny D1S force place this number at $N=88$. Octupole deformation is even less pronounced in even-even Sm ($Z=62$) nuclei; most model calculations place the boundary of the region of octupole deformation at $N=88$ Agb16 . Note that even these nuclei are very soft in octupole deformation with very little gain in binding due to octupole deformation. Thus they are transitional in nature and octupole dynamical correlations (vibrations) are expected to play an important role in their structure.

However, the situation becomes more complicated in odd and odd-odd nuclei. There are two factors which can stabilize the octupole deformation in odd and odd-odd nucleus even if its even-even core does not have static octupole deformation. These are polarization effects of unpaired particles in specific Nilsson orbitals Afana95 and rotation Naz92 . Indeed, the 5/2[413] and 5/2[523] orbitals, located in the vicinity of the proton Fermi level of the Pm isotopes of interest, couple strongly through the $Y_{30}$ operator Naz92 . However, polarization energies towards octupole deformation are weak for these orbitals for neutron numbers $N\geq 90$. So, neutron rich Pm isotopes are not expected to show static octupole deformation at low spin. On the other hand, the static octupole deformation can be stabilized by rotation even if the nucleus is only octupole soft at spin zero Naz92 . Experimental data on parity doublet bands in 151Pm and 153Eu formed by the 5/2[523] and 5/2[413] rotational structures show all features of the approach of static octupole deformation at highest observed spins Ana1993 .

In 151Pm, the opposite parity states of these two rotational sequences are connected by E1 transitions, which was interpreted as due to the presence of static octupole deformation Urban . The ground state band in 151Pm is a positive-parity K= 5/2+ rotational band based on a 5/2[413] Nilsson orbital originating from $\pi$g7/2. The negative parity band built on a K= 5/2- at an excitation energy of 117 keV is based on a 5/2-[532] Nilsson configuration originating from \pi$$h_{11/2} orbital.

In case of 153Pm, the yrast ground state band built on K= 5/2- is known to be constituted from 5/2-[532] Nilsson orbital Burke , which originates from the deformation driving \pi$$h_{11/2} orbital. In case of 151Pm, this is the non-yrast structure and the yrast ground band is 5/2+ based on 5/2+[413] configuration. Indeed, in the framework of rotation-vibration model, the level structure of 153Pm, populated by beta decay, is described as that of a deformed nucleus  Taniguchi . The single proton hole strength in 153Pm was found to be largely fragmented from the study of transfer reactions Lee . In the present work, the excited band based on a 5/2+[413] configuration in 153Pm could not be extended to higher spin and is weakly populated. It is probably due to the fact that the deformation (quadrupole) driving effect of the \pi$$h_{11/2} orbital makes 153Pm to have larger prolate deformation compared to 151Pm.

To understand the band structure in all odd-A Pm isotopes produced in the present work, the alignments Bengtsson of both favoured and unfavored signature partner bands are plotted in Fig. 20 as a function of rotational frequency. The Harris parameters Haris with J0=34.3 ${\hbar}^{2}$/MeV and J1=45.0 ${\hbar}^{4}$/MeV3 have been used to subtract the contributions of core angular momentum, which is considered as 156Gd in this case. From the alignment plot of Fig. 20, it is evident that the slopes of the alignments for the bands in 151Pm ($N=90$) are significantly different compared to all other odd-A Pm isotopes with higher N/Z. This is due to the fact that the nature of the bands in 151Pm is different as compared to corresponding bands in odd-A Pm isotopes with higher $N$. The higher alignment at higher frequency in case of odd-A Pm isotopes 153-157Pm compared to 151Pm is evident as due to the involvement of high-j $h_{11/2}$ orbital. The alignments of the bands in 155-157Pm are quite similar to that of the ground band in 153Pm, which is based on the 5/2[532] configuration originating from the $h_{11/2}$ orbital. This suggests the same 5/2[532] configuration assignment to the observed negative parity bands in 155,157Pm. In Fig. 21 the alignments of the K=5/2+ and K=5/2- bands in 153Pm are compared with the bands having same configurations and with other configurations in neighbouring $N=92$ isotones of 157Tb and 155Eu. In case of 157Tb, the 3/2+[411] band was found to be the ground state band Hartley , whereas in 155Eu 5/2+[413] band becomes the ground state band. The 5/2-[532] band, which is the ground band in 153Pm was also observed in both 155Eu and 157Tb. For the 5/2[532] band in 157Tb, the backbending occurs at the frequency $\hbar\omega\sim 0.28$ MeV due to the alignment of two $i_{13/2}$ neutrons. It can be seen that the same band in 153Pm could be observed in the present work up to the frequency corresponding to the upbend of the alignment.

The energy staggerings of the states in rotational bands of odd-$A$ 151-157 isotopes are shown in Fig. 22 as a function of spin. From the observed signature splitting it is evident that the negative parity band in 151Pm, corresponding to the 5/2-[532] orbital shows pronounced splitting compared to the positive parity band corresponding to 5/2+[413] Nilsson orbital. The odd-A Pm isotopes with higher N/Z show modest signature splitting at higher spins. The kinematic moment of inertia (J1) of the bands in odd-A Pm isotopes for both favoured and unfavoured signature partners are plotted in Fig. 23. The moments of inertia of 5/2-[532] bands in 153,155,157Pm isotopes increase at higher spins.

In order to better understand the experimental features of the observed bands, proton quasiparticle routhian diagrams for even-even nuclei neighboring to 155Pm are shown in Fig. 24. They have been obtained in the cranked Relativistic Hartree-Bogoliubov calculations (Ref. CRHB ) employing two covariant energy density functionals (CEDFs), namely, NL1 NL1 and NL3* NL3* . Although the calculated quasiparticle energies somewhat depend on the employed functional, the rotational features of the routhians of interest are independent on its choice. For example, in all panels of Fig. 24 the lowest positive parity routhians are based on the 5/2[413] orbital. These routhians are signature degenerated which is similar to the properties of the experimental 5/2[413] bands seen in 151,153Pm nuclei. The lowest two calculated pairs of negative parity routhians are based on the 5/2[532] and 3/2[514] orbitals and their rotational properties depend on the position of the proton Fermi surface. This surface is more bound in the $Z=60$ Nd nuclei. As a consequence, the 3/2[514] routhians are the lowest in energy. The interaction of hole type 3/2[514] and particle type 5/2[532] orbitals leads to substantial signature splitting in both orbitals. However, with increasing the energy of the Fermi surface on going to the $Z=62$ Sm isotopes the 5/2[532] orbital becomes the lowest in energy negative parity orbital and the coupling between the above mentioned negative parity orbitals is significantly reduced. As a consequence, the 5/2[532] orbital is signature degenerated at very low frequencies but small signature degeneracy gradually develops with increasing rotational frequency. This feature is very similar to what is seen in experimental 5/2[532] bands of 153,155,157Pm (see Figs. 21, 22 and 23). In addition to the possible role of static octupole deformation in the structure of the 5/2[532] and 5/2[413] bands of 151Pm discussed in Ref. Ana1993 , it is quite likely that large signature splitting seen in the 5/2[532] band of this nuclei is the consequence of the interaction of the 5/2[532] and 5/2[413] orbitals (seen in the upper panels of Fig. 24) which has been discussed above.

For the odd-odd Pm isotopes, the low lying high-spin isomers are interpreted in the framework of quasiparticle-rotor model as two-quasiparticle structures  Sood1990 ; Sood2011 . The proposed band structures in the present work can either be built just above the isomeric state, or above another excited state, which may exist very close to the isomeric level. Due to the lack of firm spin and parity assignment to the band structure built above the long lived isomers, reasonable configuration assignments to the observed bands cannot be made.

V Summary and Conclusions

In summary the neutron-rich 152-158Pm isotopes have been characterized using in-beam prompt $\gamma$-ray spectroscopy of isotopically identified fission fragments and high fold coincidence data of 252Cf spontaneous fission. New results of odd-odd Pm isotopes above the long lived isomeric states have been reported for the first time. The rotational band structures of odd-A Pm isotopes with neutron numbers up to $N=96$ have been extended to higher spins. The configuration asignment to the rotational structures in odd-A isotopes are understood from the systematics of band properties and in terms of routhians of the neighbouring even-even isotopes, obtained from cranked Relativistic Hartree-Bogoliubov calculations. The observed band structures of odd-A Pm isotopes do not show any indication of presence of octupole deformation beyond $N=90$.

VI Acknowledgments

We would like to thank J. Goupil, G. Fremont, L. Ménager, J. Ropert, C. Spitaels, and the GANIL accelerator staff for their technical contributions and C. Schmitt for help in various aspects of data collection, analysis and many useful discussions. The authors would also like to thank the referee for a very critical reading of the manuscript and for useful suggestions in improving the clarity of the manuscript. Two of us (S.B and S.B) acknowledges partial financial support through the LIA France-India agreement. The work at Vanderbilt University and Lawrence Berkeley National Laboratory are supported by the U.S. Department of Energy under Grant No. DE-FG05-88ER40407 and Contract No. DE-AC03-76SF00098. The work at Tsinghua University was supported by the National Natural Science Foundation of China under Grant No. 11175095. The work at JINR was partially supported by the Russian Foundation for Basic Research Grant No. 08-02-00089 and by the INTAS Grant No. 03-51-4496. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award No. DE-SC0013037 (Mississippi State University).