Measurement of cross section of the residues from the $^{11}$B-induced reaction on $^{89}$Y and $^{93}$Nb: Production of $^{97}$Ru and $^{101m}$Rh

TL;DR

This study measured production cross sections of residues from $^{11}$B reactions on $^{89}$Y and $^{93}$Nb, analyzing the data with nuclear models to understand reaction mechanisms and optimize production of medically relevant isotopes.

Contribution

It provides experimental cross section data for $^{11}$B-induced reactions on $^{89}$Y and $^{93}$Nb and evaluates the effectiveness of nuclear models in explaining these reactions.

Findings

Good agreement between measured data and Hauser-Feshbach and exciton model calculations.

Significant preequilibrium contributions in the 3n reaction channels.

Evidence of direct reaction influence in $^{90m}$Y production.

Abstract

The heavy-ion induced reactions on intermediate mass targets are complex in nature, even at the low energies. To understand those nuclear reaction phenomena in detail, more experimental studies are required in a wide range of energy. Heavy-ion reactions were investigated by measuring production cross sections of the residues produced in the $^{11}$B-induced reactions on $^{89}$Y and $^{93}$Nb at low energies, near and above the barrier, and to check the effectiveness of the different nuclear models to explain them. Further, aim is also to optimize the production parameters of neutron deficient medically relevant $^{97}$Ru and $^{101m}$Rh radioisotopes produced in those reactions, respectively. The $^{11}$B-beam was allowed to impinge on $^{89}$Y and $^{93}$Nb foils supported by an aluminum catcher foil, arranged in a stack, in 27.5-58.7 and 30.6-62.3 MeV energy range, respectively. The $\gamma$-spectrometry was carried out after EOB to measure the activity of the radionuclides produced in each foil and cross sections were calculated. Measured cross-sectional data were analyzed in terms of compound and precompound model calculations. The measured cross sections of the residues showed good agreement with the model calculations based on the Hauser-Feshbach formulation and exciton model. A substantial preequilibrium contribution was noticed in the 3$n$ reaction channel in both the reactions. Theoretical estimations confirmed that major production yields are mostly contributed by the compound reaction process. Preequilibrium emissions contributed at the high energy tail of the 3$n$ channel for both the reactions. Moreover, an indirect signature of a direct reaction influence was also observed in the $^{90m}$Y production.

Tables

Table 1. Table 1: Spectoscopic decay data nndc for the observed radioisotopes and list of contributing process in the 11 B + 89 Y and 11 B + 93 Nb reactions

Nuclides(Jπ)	Half-life	decay mode(%)	E$\gamma$(keV)	I$\gamma$(%)	Contributing reactions	Eth 222Eth denotes threshold energy.(MeV)
97Ru(5/2+)	2.83 d	$ϵ$(100 )	215.70	85.62	89Y(11B, 3n)	19.26
			324.49	10.79
95Ru(5/2+)	1.64 h	$ϵ$(100)	336.40	70.20	89Y(11B, 5n)	40.39
			626.63	17.80
96Tc(7+)	4.28 d	$ϵ$(100)	778.22	99.76	89Y(11B, p3n)	27.78
			812.54	82.00	89Y(11B, d2n)	25.28
			849.86	98.00	89Y(11B, tn)	18.25
95Tc(9/2+)	20.0 h	$ϵ$(100)	765.79	93.80	89Y(11B, p4n)	36.63
					89Y(11B, d3n)	34.13
					89Y(11B, t2n)	27.10
94Tc(7+)	4.88 h	$ϵ$(100)	702.62	99.60	89Y(11B, p5n)	47.80
			871.09	99.99	89Y(11B, d4n)	45.30
					89Y(11B, t3n)	38.26
93mMo(21/2+)	6.85 h	IT 333IT denotes isomeric transition.(99.88)	263.06	56.7	89Y(11B, $\alpha$3n)	21.21
			684.67	99.7	89Y(11B, 2p5n)	53.01
90mY(7+)	3.19 h	IT(100)	202.51	97.30	89Y(11B, 5p5n)	77.94
			479.17	90.74	89Y(11B, $\alpha$3p3n)	46.14
					89Y(11B, 2$\alpha$pn)	14.34
101Pd(5/2+)	8.47 h	$ϵ$(100)	296.29	19.00	93Nb(11B, 3n)	19.38
			590.44	12.06
100Pd(0+)	3.63 d	$ϵ$(100 )	84.02	52.00	93Nb(11B, 4n)	28.64
			126.05	7.80
99Pd(5/2+)	21.4 m	$ϵ$(100)	136.01	73.00	93Nb(11B, 5n)	41.07
			263.60	15.2
101mRh(9/2+)	4.34 d	$ϵ$(92.80),IT(7.20)	306.86	84.00	93Nb(11B, p2n)	16.29
					93Nb(11B, d2n)	13.80
					93Nb(11B, t)	6.80
100Rh(1-)	20.8 h	$ϵ$(100)	539.60	80.60	93Nb(11B, p3n)	27.36
			822.65	21.09	93Nb(11B, d2n)	24.87
			822.65	21.09	93Nb(11B, tn)	17.87
99mRh(9/2+)	4.7 h	$ϵ\left(\ge 99.84\right)$	340.71	70.00	93Nb(11B, p4n)	36.40
			617.80	12.00	93Nb(11B, d3n)	33.91
					93Nb(11B, t2n)	26.91
97Ru(5/2+)	2.83 d	$ϵ$(100)	215.70	85.62	93Nb(11B, 2p5n)	52.97
			324.49	10.79	93Nb(11B, $\alpha$3n)	21.32

Table 2. Table 2: Cross section (mb) of radioisotopes at various incident energies in the 11 B + 89 Y reaction.

Energy (MeV)
	Cross-section (mb)
	97Ru	95Ru	96Tc	95Tc	94Tc	93mMo	90mY
27.9	1.1 $\pm$ 0.6
33.2	103.6 $\pm$ 18.8
34.6	259.6 $\pm$ 46.1
37.3	353.4 $\pm$ 58.5		4 $\pm$ 1.6				0.3 $\pm$ 0.1
40.5	364.4 $\pm$ 64.2		14.9 $\pm$ 2.1	0.3 $\pm$ 0.2		1.1 $\pm$ 0.2	0.5 $\pm$ 0.1
40.7	389.3 $\pm$ 68.9		21.8 $\pm$ 3.2	0.6 $\pm$ 0.3		2.1 $\pm$ 0.6	0.6 $\pm$ 0.2
41.3	333.2 $\pm$ 55.7		29.6 $\pm$ 4.1	0.8 $\pm$ 0.4		3.1 $\pm$ 0.7	0.7 $\pm$ 0.2
45.9	280.1 $\pm$ 49.8	0.3 $\pm$ 0.2	123.9 $\pm$ 16	3.6 $\pm$ 0.8		25.9 $\pm$ 2.9	2 $\pm$ 0.6
47.1	239.4 $\pm$ 42.4	0.7 $\pm$ 0.2	116.8 $\pm$ 14.8	3.6 $\pm$ 0.8		26.1 $\pm$ 2.7	2.1 $\pm$ 0.5
50.8	131.7 $\pm$ 23.7	14.7 $\pm$ 4.6	214.3 $\pm$ 27.2	33.9 $\pm$ 6.2	0.2 $\pm$ 0.1	70.5 $\pm$ 7.5	4.2 $\pm$ 1.1
53.2	93.9 $\pm$ 16.8	25.5 $\pm$ 5.2	212.6 $\pm$ 26.5	59.6 $\pm$ 10.5	0.5 $\pm$ 0.2	79.6 $\pm$ 8.1	4.2$\pm$ 0.9
58.7	41.8 $\pm$ 7.7	93.1 $\pm$ 18.7	229.8 $\pm$ 28.7	223.2 $\pm$25.9	2.8 $\pm$ 0.6	138.3$\pm$ 13.9	7.3 $\pm$ 1.5

Table 3. Table 3: Cross section (mb) of radioisotopes at various incident energies in the 11 B + 93 Nb reaction.

Energy (MeV)
	Cross-section (mb)
	101Pd	100Pd	99Pd	101mRh	100Rh	99mRh	97Ru
30.6	20.3 $\pm$ 4.1
36	187.4 $\pm$34	9 $\pm$ 1.9		96.1 $\pm$ 35.1	2.6 $\pm$ 0.8
41	225.9 $\pm$ 40.8	63.9 $\pm$ 12.3		127$\pm$ 45.9	37.2$\pm$ 9.4		8.2 $\pm$ 1.8
41.6	229.7 $\pm$ 41.8	51.3 $\pm$ 10		139$\pm$ 50.3	27.7$\pm$ 7.1		5.3 $\pm$ 1.3
46.4	170.1 $\pm$ 31.5	134.5 $\pm$25.6		106.6$\pm$ 39.4	116.6$\pm$28.8	1.8 $\pm$ 0.6	41.3 $\pm$ 7.7
51	94.2 $\pm$ 18.3	177.5 $\pm$ 33.7	3.7 $\pm$ 1.4	54.4 $\pm$ 21.4	208.1$\pm$51.1	18.4 $\pm$ 4	101.6 $\pm$ 18.5
54.7	63.9 $\pm$ 11.7	296.9 $\pm$ 65.4	13.3 $\pm$ 5.1	54.7 $\pm$ 20.6	302.8 $\pm$ 73.3	80.5$\pm$16.1	183.6 $\pm$ 32.4
58.5	38.3 $\pm$ 7.4	260.5 $\pm$ 58.6	32.1 $\pm$ 11.6	28.1 $\pm$ 11.9	327 $\pm$ 79.2	199.8$\pm$40.1	240.2 $\pm$ 42.5
62.3	21.1 $\pm$ 4.4	170.5 $\pm$ 40.1	42.5 $\pm$ 15.1	12.7 $\pm$ 6.5	258.4 $\pm$ 62.6	301.4$\pm$59.7	236.5 $\pm$ 41.7

Equations

$$\sigma^{HF}_{\alpha\beta}(E_{\alpha})=\sum_{J,\Pi}\bigg{[}\pi\lambdabar^{2}\frac{2J+1}{(2s+1)(2I+1)}\sum_{j,l}T_{\alpha jl}(E_{\alpha},J,\Pi)\bigg{]}\bigg{[}\frac{\sum_{j^{\prime},l^{\prime}}T_{\beta j^{\prime}l^{\prime}}(E_{\beta},J,\Pi)}{\sum_{\gamma,j^{\prime\prime},l^{\prime\prime}}T_{\gamma j^{\prime\prime}l^{\prime\prime}}(E_{\gamma},J,\Pi)}\bigg{]}$$

$${\sigma }_f=\pi {\text{lambdabar}}^2\sum _l(2l+1)T_l$$

$$\frac{d{\sigma }_{\alpha ,\beta }}{d{ϵ}_{\beta }}={\sigma }^{CF}({ϵ}_{\alpha })\sum _n{W}_{\beta }(E,n,{ϵ}_{\beta })\tau (n),$$

$$W_{\beta}(E,n,\epsilon_{\beta})=\frac{2s_{\beta}+1}{\pi^{2}\hbar^{3}}\mu_{\beta}\epsilon_{\beta}\sigma^{inv}_{\beta}(\epsilon_{\beta})\bigg{[}\frac{\sum_{\beta}F^{\beta}_{lm}(\epsilon_{\beta})Q_{\beta}^{lm}(p,h)\omega_{res}(p-l,h,E-\epsilon_{\beta}-B_{\beta})}{\omega_{CN}(p,h,E)}\bigg{]}$$

$$H(r,\zeta )=-\frac{{\hslash }^2{\nabla }^2}{2\mu }+V(r)+H^0(\zeta )+H^{\prime }(r,\zeta )$$

$$\bigg{(}-\frac{\hbar^{2}}{2\mu}\frac{d^{2}}{dr^{2}}+\frac{J(J+1)\hbar^{2}}{2\mu r^{2}}+V(r)-E+\epsilon_{n}\bigg{)}u^{J}_{n}(r)=-\sum_{n^{\prime}}H^{\prime}_{nn^{\prime}}(r)u^{J}_{n^{\prime}}(r)$$

$$T_J(E)=\sum _I|P_{I{I}^{\prime }}^J(E){|}^2$$

Full text

The heavy-ion induced reactions on intermediate mass targets are complex in nature, even at the low energies. To understand those nuclear reaction phenomena in detail, more experimental studies are required in a wide range of energy.

Purpose

Investigation of heavy-ion reactions by measuring production cross sections of the residues produced in the 11B-induced reactions on 89Y and 93Nb at low energies, near and above the barrier, and to check the effectiveness of the different nuclear models to explain them. Further, aim is also to optimize the production parameters of neutron deficient medically relevant 97Ru and 101mRh radioisotopes produced in those reactions, respectively.

Method

The 11B-beam was allowed to impinge on 89Y and 93Nb foils supported by an aluminum (Al) catcher foil, arranged in a stack, in 27.5–58.7 and 30.6–62.3 MeV energy range, respectively. The off-line $\gamma$-spectrometry was carried out after the end of bombardment (EOB) to measure the activity of the radionuclides produced in each foil and cross sections were calculated. Measured cross-sectional data were analyzed in terms of compound and precompound model calculations.

Results

The measured cross sections of 97,95Ru, 96,95,94Tc, 93mMo, 90mY radionuclides produced in the 11B+89Y reaction, and 101,100,99Pd, 101m,100,99mRh, 97Ru produced in the 11B+93Nb reaction showed good agreement with the model calculations based on the Hauser-Feshbach formulation and exciton model. Unlike theoretical estimation, consistent production of 90mY was observed in the 11B+89Y reaction. Substantial preequilibrium contribution was noticed in the 3$n$ reaction channel in both the reactions.

Conclusions

Theoretical estimations confirmed that major production yields are mostly contributed by the compound reaction process. Preequilibrium emissions contributed at the high energy tail of the 3$n$ channel for both the reactions. Moreover, an indirect signature of a direct reaction influence was also observed in the 90mY production.

I Introduction

The comprehensive study on fusion reactions of tightly and weakly bound stable heavy projectiles with medium and heavy targets has been performed and discussed in the literature for many decades back14 ; canto15 . However, strength of reaction processes, such as complete-incomplete fusion, deep inelastic scattering, quasifission, precompound processes near the Coulomb barrier, nucleon transfer reactions etc., observed in the low-energy heavy ion induced reactions have not yet been understood in a full-fledged fashion parker91 ; kelly00 ; dasgupta04 ; zolnowski78 ; timmers98 ; vergani93 ; sharma15 ; shrivastava06 . In spite of that, its importance to understand the synthesis of superheavy elements hinde11 ; hinde08 , nucleosynthesis process necessary for the star evolutionwallerstein97 , quantum mechanical tunneling phenomenon near sub-barrier energies, fusion hindrance phenomenon at deep sub-barrier energies jiang05 ; stefanini08 , behavior of nuclei far from the stability region investigated using radioactive ion beam on the medium/heavy mass targets rehm98 ; vinod13 ; signorini97 , etc. fascinate researchers and make it a central topic for nuclear physics research in recent years.

In view of this quest, a systematic study of boron (11B) induced reaction on intermediate mass targets: yttrium(89Y) and niobium(93Nb), has been reported in the $\sim$2.5–5.5 MeV/nucleon energy range. Production of 97,95Ru, 96,95,94Tc, 93mMo, 90mY and 101,100,99Pd, 101m,100,99mRh, 97Ru radionuclides are observed at 89Y and 93Nb targets, respectively. This article contributes to study the nuclear reaction mechanisms involved in the production of various radioisotopes. It is also important to examine the reaction cross section predictive capability of recent upgrades in modern reaction codes for model calculations. Optimization of the production of neutron deficient medically relevant radionuclides, 97Ru and 101mRh, which are produced in 11B+89Y and 11B+93Nb reactions, respectively, has also been discussed.

The 97Ru radionuclide could be used in both diagnostic and therapeutic processes due to its suitable half-life (2.83 d), low-lying intense $\gamma$-rays: 215.70 keV (85.62%) and 324.49 keV (10.79%) energy, and high chemical reactivity. It could be produced in the no-carrier-added (NCA) state, which is the prerequisite of clinical applications maiti09 , from 11B+89Y reaction. Initially, 97Ru was produced mainly by the bombarding high energy proton beams on different targets: rhodium (103Rh), technetium (99Tc), srivastava78 ; lagunas83 ; zaitseva92 . Besides, $\alpha$-particle or 3He induced reactions on natural molybdenum targets were also led to the production of 97Ru comar76 ; omperetto80 ; pao81 . Recently, heavy ion (7Li, 11B, 12C) induced reactions on natural Nb and Y metals were also studied by our group to produce NCA 97Ru maiti11 ; maiti15 ; maiti13 ; deepak16 ; dkumar17 .

On the other hand, low-lying high intense $\gamma$-rays of 101mRh help in the $in\ vivo$ monitoring by using a scintillation camera, while emission of Auger, Coster-Kronig electrons and X-rays aid in therapeutic applications. The 101mRh (4.34 d) decays mainly by electron capture (92.8 %) to stable 101Ru by emitting 306.9 keV (81 %) and 545.1 keV (4.3 %) $\gamma$-rays and by isomeric transition (IT) (7.2 %) to 101Rh (3.3 a), which finally decays to 101Ru.

So far, production of 101mRh has been studied using light ion ($p$, $d$, 3He, 4He) induced reactions only. 101mRh was produced through the decay of its precursors 101Pd and 101Ag, which were populated in $p$-induced reactions on the 103Rh, natPd, and natAg targets scholtz77 ; lagunas82 ; lagunas84 ; ditroi07 ; hermanne00 ; sudar02 ; uddin05 . In the deuteron-induced reactions, production of 101mRh using 103Rh target was measured by Hermanne $et$ $at.$, Detr$\acute{o}$i $et$ $al.$ in different energy regions hermanne02 ; ditroi11 ; hermanne15 . Direct and cumulative production of 101mRh in the d+natPd reaction was also experimented by Detr$\acute{o}$i $et$ $al.$ ditroi12 , however the production was significantly low. Apart from these, production of 101mRh isomer was reported by Skakun $et$ $al.$ skakun08 for the 3He-induced reaction via 101Ru(3He,$x$)101mRh (cum) and 102Ru(3He,$x$)101mRh reactions.

Thus we have gone through the current interest to study the heavy ion induced reactions and the production of 97Ru and 101mRh radionuclides in those reactions. The experimental procedure and brief review of the nuclear model calculations are described in Secs. II and III, respectively. Section IV discusses the results and Sec. V finally concludes the report.

II Experiment

The experiment was performed at the BARC-TIFR Pelletron facility, Mumbai, India. Stacked foil activation technique was used to explore 89Y+11B and 93Nb+11B reactions. A stack of targets was prepared by placing 2-3 target foils each one of which was backed by an aluminum (Al) catcher foil so that target and backing appear in an alternative fashion. A typical experimental setup to irradiate the stack foil arrangement is shown in Fig 1. Each target stack was bombarded by the 11B5+ beam for a stipulated time. Beam current was kept almost constant during the experiment. The total charge passed through the target was measured by an electron suppressed Faraday cup placed at the back of the target assembly during the beam-on period. The time of irradiation was decided by the projectile flux and the half-lives of the product radioisotopes. A total of 4-5 such stack was irradiated individually for each target-projectile combination varying the incident energy of 11B with a slight overlap between them.

Spectroscopically pure (99.99%) natural yttrium and niobium foils were procured from the Alfa Aesar. Self-supporting thin foils of those metals were made by uniform rolling in a machine. Thicknesses of the thin Y- and Nb-foils were between 0.84-2.9 mg/cm2 and 1.2-2.1 mg/cm2, respectively. The Al-backing foils had thickness between 1.5-2 mg/cm2. Annular aluminum holders with an inner and outer diameter 12 and 20 mm, respectively, were used to mount the foils. The large area of Al foil ensures the complete collection of recoiled the residues, if recoiled any, in the beam direction. The Al-foils also served the purpose of an energy damper so that suitable energy separation between consecutive target foils could be achieved. Energy degradation of the projectile in each foil was estimated by Stopping and Range of Ions in Matter (SRIM) code ziegler10 . The 11B energy at a target is typically the average of the incident and outgoing beam energy.

After the end of bombardment (EOB), the residual radionuclides produced in each target foil (Y and Nb) were identified and quantified with the help of $\gamma$-ray spectrometry using a broad energy germanium (BEGe) based detector attached with a PC operating with the GENIE-2K software. The detector was calibrated by using standard sources, 152Eu (13.506 a), 137Cs (30.08 a), 60Co (5.27 a), 133Ba (10.51 a), of known activity. The energy resolution of the detector was $\leq$ 2.0 keV at 1332 keV energy.

The activity of the residuals was measured in a fixed geometry over a longer period of time in the regular intervals to follow their decay profile. The activity of the residuals at the EOB was measured from the background-subtracted peak area count rate (counts/sec). Production cross section of the residues at each incident energy was calculated from the activation formula. The detail description of the activity and cross-section measurement is available in our previous reports deepak16 ; ms11 ; m11 . Nuclear spectroscopic data of the residual radionuclides are listed in Table 1 nndc .

The error introduced in the cross section measurement was mainly due to non-uniformity of samples and in measuring its thickness ($\sim$5%), fluctuation of beam current ($\sim$5%), efficiency calibration of the detector ($\sim$2%). Some other sources such as the branching intensity of characteristic $\gamma$-rays, counting statistics, beam energy degradation while traversing through the successive target foils (straggling effects) etc. are also responsible; however, these were negligible in this case wilke76 ; kemmer80 . The total uncertainty associated with the cross section measurement was determined considering all those factors and the data was presented in this article up to 95% confidence level.

III Analysis of measured data

III.0.1 PACE4

Compound reaction contribution in the produced residues at different bombarding energies in the 11B+89Y and 11B+93Nb reactions was extracted with the help of a statistical model code PACE4 gavron80 , build on the Hauser-Feshbach (HF) formulation where angular momentum coupling is considered in each stage of de-excitation of an excited compound nucleus. The compound nucleus cross section has the form

[TABLE]

where $\lambdabar$ ($=\lambda/2\pi$) is the wavelength of incident projectile; $s$, $I$ and $J$ represent projectile, target and compound nucleus spin, respectively, and $l$ is orbital angular momentum of the projectile. $T_{\alpha jl}(E_{\alpha},J,\Pi)$ stands for the transmission coefficient having channel energy $E_{\alpha}$ and orbital angular momentum $l$, which together with particle spin $s$ couples to the channel angular momentum $j$ used to select in target nucleus spin $I$ populated for a given compound nucleus spin $J$ and parity $\Pi$. Similarly, $T_{\beta j^{\prime}l^{\prime}}(E_{\beta},J,\Pi)$ and $T_{\gamma j^{\prime\prime}l^{\prime\prime}}(E_{\gamma},J,\Pi)$ indicate transmission coefficients for $\beta$ and $\gamma$ channels with emitting energies $E_{\beta}$, $E_{\gamma}$ and orbital angular momenta $l^{\prime}$, $l^{\prime\prime}$ couple with emitting particle spins gives channel spins $j^{\prime}$, $j^{\prime\prime}$, respectively. The quantity in the first square bracket indicates the compound nucleus formation/fusion cross section in a state of total spin ($J$) and parity ($\Pi$) associated to the incident channel $\alpha$ which reduces to a simple form for spin less target ($I=0$),

[TABLE]

The quantity in the second square bracket represents the decay probability of the compound nucleus in the channel $\beta$ having ejectile particle energy $E_{\beta}$.

PACE4 uses Bass model potential bass77 for the calculation of transmission coefficient, although it is not well suited near/below the barrier as well as for very heavy ion projectiles. Fission is considered as a decay mode, and modified rotating liquid drop fission barrier (by A. J. Sierk) is selected. Evaporation of seven light particles/nuclei in the order n, p, $\alpha$, d, t, 3He, 6Li is considered whose transmission coefficients are determined by optical model potential, where optical model parameter is taken from Ref perey76 . Gilbert Cameron (GC) nuclear level density parameter and GC spin cutoff parameter are adopted for the calculation. Little a ratio, af/aγ, is taken as unity. In order to simulate $\gamma$ multiplicity and corresponding energy, a non-statistical yrast cascade gamma decay chain is artificially included.

III.0.2 EMPIRE3.2

EMPIRE considers all three major nuclear reaction formalisms - Direct (DIR), Preequilibrium (PEQ) and Compound (EQ). DIR processes are estimated either by coupled channels approach or distorted wave Born approximation (DWBA) raynal ; raynal72 . There are various PEQ phenomenological and quantum models for light-ion induced reactions. However, PEQ emissions in the heavy-ion induced reactions are not well tested for phenomenological hybrid Monte Carlo simulation as well as quantum mechanical multi-step direct (MSD) and multi-step compound (MSC) models, and therefore ignored by the code. PEQ emission for heavy ion projectiles is calculated using the exciton model, which has the capability to treat the cluster emission built on the Iwamotto Harada model iwamoto82 . The differential cross section of the PEQ emission has a form

[TABLE]

where $\sigma^{CF}(\epsilon_{\alpha})$ is the composite nucleus formation cross section and defined as $\sigma^{CF}(\epsilon_{\alpha})=\sigma_{reac}(\epsilon_{\alpha})-\sigma_{dir}(\epsilon_{\alpha})$, a difference of reaction and direct reaction cross section. $\tau(n)$ is life-time of $n$ exciton configuration. $W_{\beta}(E,n,\epsilon_{\beta})$ represents the emission rate of a cluster $\beta$ with energy $\epsilon_{\beta}$, spin $s_{\beta}$ and reduced mass $\mu_{\beta}$ from a state with $n\ (=p+h)$ excitons and can be given as,

[TABLE]

where $\sigma^{inv}_{\beta}(\epsilon_{\beta})$ is the inverse reaction cross section; $\omega(p,h,E)$ is particle-hole state density, calculated by Williams formula williams71 . $Q_{\beta}^{lm}(p,h)$ is a factor accounting for the probability of the outgoing cluster $\beta$ being formed with $l$ particles situated above and $m$ below the Fermi surface ($\beta=l+m$) and factor $F^{\beta}_{lm}(\epsilon_{\beta})$ denotes formation probability of the cluster $\beta$ as a function of its energy.

EQ processes are calculated from the Hauser-Feshbach model, including width fluctuations and the optical model for fission. However, heavy ion fusion cross section is estimated with the help of a simplified coupled channel model (CCFUS) dasso87 . In CCFUS, collision between two nuclei is considered in the presence of coupling of the relative motion $\vec{r}$ of the projectile to a nuclear collective motion $\zeta$. The Hamiltonian of such system is written as hagino12

[TABLE]

where $\mu$ is the reduced mass of the system and $V(r)$ is the sum of Coulomb and nuclear Woods-Saxon potential. $H^{0}(\zeta)$ and $H^{\prime}(r,\zeta)$ stand for the intrinsic and coupling Hamiltonian, respectively. The coupled-channels equations for the radial part of the total wave function can be written from such Hamiltonian as

[TABLE]

where $n$ represents a nth quantum state and $\epsilon_{n}$ is the energy eigenvalue of the intrinsic Hamiltonian. $J$ is the total angular momentum, the sum of relative orbital angular momentum $l$ and the angular momentum of intrinsic motion $I$. $H^{\prime}_{nn^{\prime}}$ = \big{<}n\big{|}H^{\prime}\big{|}n^{\prime}\big{>} is the coupling matrix element. Diagonalizing this matrix element at the barrier, the matching wave functions can be uncoupled roughly. The total transmission probability is obtained by summing over the distribution of transmission probabilities for the eigenbarriers, with weight given by the overlap of the initial state with eigenchannels,

[TABLE]

where $I^{\prime}$ is the angular momentum of collective motion in the entrance channel. Thus the fusion cross section can be calculated by using Eq. 2 except that the transmission probability is now affected by each reaction channel.

In the present calculation, the value of the mean free path parameter for the exciton model is chosen as 1.5 and the equilibrium exciton number varies between 10–14 for 25–65 MeV energy range of the projectile. The complete fusion cross section is calculated up to 21–46 $l_{max}$ value for 25–65 MeV energy range using Christensen-Winther potential christensen76 . Various nuclear level density options: Gilbert Cameron (GC) level density with Ignatyuk systematic, Generalized Superfluid Model (GSM), and Enhanced Generalized Superfluid Model (EGSM) have been used.

In all the three level density model, Ignatyuk level density parameter, which consists of two independent parameters: asymptotic value of the level density parameter ($\tilde{a}$) and shell effect damping parameter ($\gamma_{s}$), is used. In GC model, Ignatyuk systematic is used in which $\tilde{a}$ = 0.154A + 6.3$\times$10*-5A2* and $\gamma_{s}$ = -0.054. GSM and EGSM use $\tilde{a}$ = $\alpha$A + $\beta$A2/3 and $\gamma_{s}$ = $\gamma_{0}$A1/3 where $\alpha$ = 0.103, $\beta$ = -0.105, $\gamma_{0}$ = 0.375 are used for GSM and $\alpha$ = 0.0748, $\beta$ = 0.0, $\gamma_{0}$ = 0.5609 are used for EGSM.

IV Results and discussion

A methodical investigations of radioisotopes produced in the 11B-induced reaction on 89Y and 93Nb targets were carried out for each target foils at various incident energies. Two typical $\gamma$-ray spectra collected 38.3 and 37.9 minutes after the EOB from the 11B+89Y and 11B+93Nb reactions at 50.8 and 51 MeV incident energies are shown in Figs 2 and 3, respectively. Production of 97,95Ru, 96,95,94Tc, 93mMo, 90mY residues in the 89Y; and 101,100,99Pd, 101m,100,99mRh, 97Ru radionuclides in the 93Nb target matrix are confirmed and are presented in Figs 4–10, and Figs 11–18, respectively. Measured data points are indicated by symbols with an uncertainty and the theoretical estimations are shown by curves.

The measured cross sections are compared with the theoretical model calculations from PACE4 and EMPIRE3.2 utilizing different nuclear level density options. A list of the radionuclides and the possible contributing reactions are listed in Table 1 nndc . Experimental cross section data are tabulated in Table 2 and Table 3 for the 11B + 89Y and 11B + 93Nb reactions, respectively.

IV.1 Radionuclides produced in 11B+89Y

IV.1.1 97,95Ru

The measured excitation function of 97Ru, presented in the Fig 4, is compared with the PACE and EMPIRE calculation. Experimental data are well reproduced by both the model codes in the lower energy region ($\sim$28–42 MeV), however, PACE estimation sharply decreases compared to the measured data at higher energies and becomes about 20 times smaller than the experimental cross section at 58.7 MeV energy. The experimental results are in good agreement with those computed from the EMPIRE at the high energy region. It certainly indicates the emission of PEQ neutrons, along with evaporated neutrons in the 3$n$ reaction channel, as observed in various heavy-ion induced reactions vergani93 ; sharma15 ; deepak16 . Reproduction of the data describes the necessity of the PEQ exciton model used in EMPIRE for heavy projectiles. Although all the level densities show a good agreement between each other, GSM level density reproduces the measured data more accurately in comparison to the EGSM and GC level densities at high energy tail of the excitation function.

Figure 5 shows a comparison between the measured cross sections of 95Ru in the 45–60 MeV energy range and the theoretical evaluation. Experimental cross sections are best explained by EMPIRE with GSM level density throughout the energy range, while other two calculations with EGSM and GC level density overestimate the measured data in the high energy range ($\sim$52–60 MeV). On the other hand, PACE result underpredicts the experimental data below 52 MeV and overpredicts above it. Independent productions of 97,95Ru are measured due to the absence of any precursor.

IV.1.2 96,95,94Tc

Out of the two isotopes, 96,96mTc, the ground state of the long-lived 96Tc (4.28 d) was identified. Direct identification of the 96mTc (51.5 m) radionuclide is hardly possible due to its single low intense $\gamma$-ray (778.22 keV, 1.9% intensity) common with the high intensity (99.76%) 778.22 keV peak of 96Tc. EMPIRE predicts the maximum 6% production of 96mTc compared to 96Tc production. It is expected that activity of 96Tc must increase in 5–6 h cooling time due to the decay of 96mTc (IT–98%), if produced in the target matrix, into 96gTc radionuclide, however, no such sign was observed. Experimental and theoretical excitation functions of the 96Tc is shown in Fig 6. Both PACE4 and EMPIRE data reproduce the experimental results satisfactorily in the lower energy region, but overestimate in the high energy region.

In the Fig 7, experimental cross sections of the short-lived 95Tc (20.0 h) are shown along with the theoretical excitation functions. The measured data are satisfactorily reproduced by the EMPIRE and PACE4 in the higher energy region, while PACE underpredicts them in the lower energy range. EMPIRE calculation corresponding to EGSM and GC has shown the best reproduction of measured data throughout the estimated energy range. Cumulative production of 95Tc may be possible from 95Ru radionucides via electron-capture ($\epsilon$-decay) process. However, trace of 95mTc was not observed in this experiment.

The 94Tc radionuclides may be produced in both meta-stable state 94mTc (52 m) and ground state 94Tc (4.88 h). Due to the common $\gamma$-ray peak at 871.09 keV of 94mTc and 94Tc radionuclides, it is not possible to identify 94mTc radionuclides directly. However EMPIRE predicts significantly low isomeric 94mTc cross section compared to 94Tc. The measured excitation function of 94Tc, shown in Fig 8, is well reproduced by EMPIRE with GC level density while another two level densities overestimate the measured data, particularly at the higher energy region. PACE is unable to explain the experimental observation throughout the observed energy region.

IV.1.3 93mMo

The excitation function of 93mMo is plotted in Fig 9 to compare with the PACE and EMPIRE calculations. Experimental data are well reproduced by the EMPIRE with the EGSM level density option throughout the energy range considered. Calculations of EMPIRE using other two level densities are found satisfactory below 47 MeV projectile energy and underpredict the data above it. As the code PACE calculates the cross section of 93Mo, the sum of isomeric and ground state, it overpredicts the experimental data throughout (up to 55 MeV) the energy.

IV.1.4 90mY

A consistent production of 90mY radionuclide observed in the 11B+89Y reaction is shown in the Fig 10. The PACE4 estimation is for 90Y, hence it overpredicts the EMPIRE calculation which is for 90mY. The trend of the measured excitation function is similar to those obtained from the theoretical cross sections, however, theoretical estimation is almost 10 times lower than the experimental results. Perhaps production of 90mY is an indication towards the neutron transfer from the projectile to the yttrium target.

IV.2 Radionuclides produced in 11B+93Nb

IV.2.1 101,100,99Pd

A comparison between the measured and theoretical excitation functions of 101Pd is shown in Fig 11. It is observed that PACE satisfactory explains the measured data below 47 MeV incident energy and falls considerably beyond it. Overall, experimental observation is well reproduced by EMPIRE with EGSM level density within experimental uncertainties, however small deviation is observed above 52 MeV impinging energy. Similar to that of $3n$ channel reaction in 11B+89Y, precompound emission of neutrons is observed over the compound reaction mechanism at the high energy tail of the excitation function. This direct production of 101Pd is contributed by both precompound and compound nuclear processes.

Production of 100Pd and 99Pd at different incident energies are indicated in Fig 12 and Fig 13, respectively, to compare with the theoretical results. It is evident from the Fig 12 that PACE calculation underpredicts the data at the lower energies and overpredicts at the higher energy range. Experimental data are well reproduced by the EMPIRE calculation with EGSM level density throughout the energy range within the experimental error. EMPIRE estimation with GC level density overestimates the measured data, while that with the GSM level density well reproduces up to 43 MeV energy and underestimates beyond it. On the other hand, in the Fig 13, none of the model calculation explained the experimental observations, although EMPIRE calculations mimic the trend well.

IV.2.2 101m,100,99mRh

101mRh can be produced in the target matrix either by independent reaction channels or through the decay of its precursor, 101Pd. Due to the comparatively shorter half-life, 101Pd (8.47 h) would decay to 101mRh (4.34 d), hence cumulative production would increase if a long cooling time is allowed. Cumulative yield of 101mRh in different half-lives of 101Pd has been shown in Fig 14 for various projectile energies. Exponential increment of the cross-section through the decay of its higher charge isobar (101Pd) has been observed with the passage of time, as expected. On an average, $\sim$55% increment in the cross section of 101mRh is observed for all the energies at the first half-life of 101Pd after the EOB. However, independent production cross-sections of 101mRh is measured in this work and the excitation function is shown in Fig 15. PACE explains the data up to 51 MeV incident energy and underpredicts above it. EMPIRE calculations with EGSM and GC level density reproduce the experimental data within the error bar over the energy region, while GSM overestimates beyond 40 MeV projectile energy. Nevertheless, EMPIRE calculation shades light on the role of the PEQ reaction mechanism to 101mRh at the high energy tail.

The 100Rh has a metastable state 100mRh (4.6 m, IT = 98.3 % and $\epsilon$ = 1.7 %) and a relatively long lived ground state 100Rh (20.8 h). Metastable 100mRh could not be identified due to its short half-life. Thus measured cross section of 100Rh is the collective cross section contributed by the independent production routes and the decay from 100mRh, if it was produced. Various possible production routes of 100Rh are listed in Table 1. Fig 16 shows a comparison between the measured data and the calculations for 100Rh. EMPIRE calculations satisfactorily predict the experimental results, while PACE calculation shows a small deviation both in lower and higher energy side. EMPIRE with EGSM has best reproduced the experimental results. Although decay of 100Pd (3.63 d) could add to the cross section of 100Rh, this possibility was avoided recording the $\gamma$-ray spectrum immediately after the EOB.

The metastable 99mRh (4.7 h) that mainly decays to stable 99Ru ($\epsilon$ $\geq$ 99.84 %) was produced in the target matrix. EMPIRE calculation also support the isomeric production along with minute production of ground state 99Rh. The measured excitation function of 99mRh is shown in the Fig 17 and compared the isomeric production obtained from EMPIRE along with the PACE that calculates the sum of isomeric and ground state production. EMPIRE with GC explains the experimental result slightly better than EGSM and GSM level density calculation. PACE grossly underestimates the measured excitation function throughout the entire energy range.

IV.2.3 97Ru

Fig 18 represents a comparison between experimental data of 97Ru and the theoretical estimations. Measured results are best described by the EMPIRE with EGSM level density. EMPIRE estimate with GC underpredicts and that with GSM overpredicts the measured excitation function above 52 MeV impinging energy. PACE data satisfactory explain the experimental observation.

In general, measured cross section data is well reproduced by EMPIRE over PACE4. In the low energy region, a gradual increase in the theoretical cross sections of the radionuclides is observed in EMPIRE calculations compared to the steep increment in PACE4. It might be due to the more accurate treatment of fusion cross section (CCFUS) calculation and a general consideration of Ignatyuk energy-dependent level density parameter in EMPIRE. Moreover, EMPIRE successfully explained the PEQ emission of particles in both the reactions using exciton model over the compound process. Though the effectiveness of the level density models (EGSM/GSM/GC) could not be concluded precisely from this study, yet GSM/EGSM explains satisfactory most of the reaction channels.

IV.3 Medically relevant radionuclides

Significant cross section (above 200 mb) of 97Ru radionuclide is observed in the 34.6–47.1 MeV wide energy spectrum in which 40.7 MeV projectile energy witnessed the maximum production cross section of $\sim$ 389 mb. Production of most of the contaminants such as 95Ru, 94Tc, 93mMo and 90mY are negligibly small in the desired energy range and would ultimately decay out due to their short half-lives. Therefore, only 97Ru and 95Tc will be abundant after a day, which can be separated chemically maiti13 ; maiti15 ; dkumar17 .

On the other hand, production of 101mRh (direct and cumulative ) is possible within 36–51 MeV energy range in the 11B+93Nb reaction. Maximum production cross sections of 101mRh (139 mb) and its precursor 101Pd (229.7 mb) that decays into 101mRh is measured in the 41.6 MeV energy. A significant quantity of 101mRh could be achieved after an appropriate cooling time.

It is true that heavy ion reactions cannot compete with the light ion production routes (of 97Ru, 101m) in terms of the production yield. However, sufficient production of those radionuclides is possible to conduct the experiments in the laboratory scale. A good quantity of those radionuclides could be produced using a high current heavy ion accelerator.The significance of the heavy ion induced production route of 97Ru and 101mRh from the target matrices Y and Nb, respectively, and their subsequent chemical separation procedures have been discussed in detail in our recent articles dkumar17 ; dm17 .

V Summary

For the first time, a detailed investigation of the excitation functions of the evaporation residues produced in the 11B-induced reaction on 89Y and 93Nb targets were carried out and the theoretical support was provided in order to extract information about their production mechanism. It might be helpful to optimize the production parameters of medically relevant radionuclides: 97Ru, 101mRh. A comparative study of the various level density models (GSM/EGSM/GC) used in EMPIRE is reported in this article. Although, no specific level density model could be suggested to explain the 11B+89Y and 11B+93Nb reaction data, EGSM/GSM calculations reproduced the measured data in many channels. In general, EMPIRE calculations show better reproduction of the cross sections in most of the channels. The comparisons of the theoretical model calculations suggest that the compound reaction mechanism is the dominant route for the production of residues. Like other heavy-ion induced reactions, PEQ emission of neutrons was observed in the $3n$ channels for both the reactions. A signature of PEQ emission was also evident in the $p2n$ and $p3n$ channel in 11B+93Nb reaction. Unlike theoretical expectation, a steady and substantial production of 90mY radionuclides was observed at all energies which might be the consequence of the neutron transfer processes in 11B+89Y reaction. Satisfactory reproduction of measured data by the EMPIRE calculations indicate the dependence of collective effects, considered in EGSM/GSM level density, on the compound and PEQ processes and the effectiveness of CCFUS calculations used for heavy ion fusion cross section.

Acknowledgements.

Authors sincerely acknowledge the technical help and cooperation received from Professor S. Lahiri, SINP, Kolkata, during the experiment, and also thank the Pelletron staff, target laboratory staff of the BARC-TIFR Pelletron facility for their assistance during the experiment. Fellowship from MHRD; grants of IITR/SRIC/218/FIG, Government of India, are gratefully acknowledged.