First investigation on the isomeric ratio in multinucleon transfer reactions: Entrance channel e ff ects on the spin distribution

The multinucleon transfer (MNT) reaction approach was successfully employed for the first time to measure the isomeric ratios (IRs) of 211 Po (25 / 2 + ) isomer and its (9 / 2 + ) ground state at the IGISOL facility using a 945 MeV 136 Xe beam impinged on 209 Bi and nat Pb targets. The dominant production of isomers compared to the corresponding ground states was consistently revealed in the α -decay spectra. Deduced IR of 211 Po populated through the 136 Xe + nat Pb reaction was found to enhance ≈ 1.8-times than observed for 136 Xe + 209 Bi. State-of-the-art Langevin-type model calculations have been utilized to estimate the spin distribution of an MNT residue. The computations qualitatively corroborate with the considerable increase in IRs of 211 Po produced from 136 Xe + nat Pb compared to 136 Xe + 209 Bi. Theoretical investigations indicate a weak influence of target spin on IRs. The enhancement of the 211 Po isomer in the 136 Xe + nat Pb over 136 Xe + 209 Bi can be attributed to the di ff erent proton ( p )-transfer production routes. Estimations demonstrate an increment in the angular momentum transfer, favorable for isomer production, with increasing projectile energy. Comparative analysis indicates the two entrance channel parameters, projectile mass and p -transfer channels, strongly influencing the population of the high-spin isomer of 211 Po (25 / 2 + ). This work is the first experimental and theoretical study on the IRs of nuclei produced via di ff erent channels of MNT reactions, with the latter quantitatively underestimating the former by a factor of two.


Introduction
The crux of exploring nuclear reaction and structural properties of heavy neutron-rich nuclei is to grasp an understanding of the evolution of shell structure far from the valley of β-stability, which in turn is crucial for the astrophysical rapid neutron capture process (r-process) [1][2][3].Of all the nuclear properties, experimental data on isomeric ratios (IRs) of reaction products is essential to comprehend the spin distributions, which eventually affect the population of isomers.Knowledge of the proper production routes of exotic neutron-rich isomers is vital for studying nuclear structural aspects like half-lives, spins, decay paths, etc., which may play a prominent role in driving the r-process pathways [4,5].Moreover, nuclear isomers can be exploited for applications like nuclear medicine, energy storage, etc. [6][7][8][9][10].
The strenuous attempt to overcome experimental challenges in the production, separation, and identification of heavy MNT fragments is still being continued across various nuclear laboratories around the globe [44][45][46].Several ion-catcher setups have been commissioning in recent years to span a broader coverage of angular distribution of MNT products (e.g., ≈20 • -60 • , [47]), such as MNT-ion gas cell at IGISOL [48,49], FRS ioncatcher (IC) with INCREASE at GSI [46,50], N=126 factory at ANL [51], and NEXT at Groningen [52].The KISS experiment at Riken has recently led to breakthroughs by measuring an unknown uranium isotope, 241 U, together with many neutron-rich projectile-like fragments (PLFs) of Pa-Am isotopes in an MNT reaction of 238 U+ 198 Pt [53].Moreover, spectroscopic investigations on several target-like fragments (TLFs) of Os-Pt isotopes in many experiments of 136 Xe+ 198 Pt have built up promising prospects for the MNT methodology to produce many more undiscovered nuclei [54][55][56][57].In this endeavor, a comprehensive and systematic program for MNT reactions using newly developed different types of MNT-ion catchers at IGISOL (JYFL) and FRS-IC (GSI) facilities have been initiated in the interest of addressing both aspects of nuclear features: (i) to disentangle the MNT reaction processes in addition to benchmarking state-of-the-art MNT models; and (ii) to produce neutron-rich exotic isotopes and isomers for nuclear structural studies and mass measurements [46,49,[58][59][60][61][62].
Recent MNT models differ by orders of magnitude for the nuclei produced by transferring a few nucleons from the target/projectile (e.g., ∆Z ≥ 2) or for symmetric target-projectile systems [32][33][34][35].This generates urgent interest in validating these models by comparing them with the reaction data of different forms.This letter reports the first measurements of IRs populated via the MNT reactions.The IR manifests the characteristics of the spin distribution of MNT fragments.Moreover, computations of the spin distribution of the MNT fragment are performed for the first time using improved state-ofthe-art Langevin-type model calculations and benchmarked by comparing it with the measured IRs.

Experimental study
A series of experiments were performed during the commissioning of dedicated MNT gas cells with the aim of accessing neutron-rich exotic nuclei utilizing the MNT approach at the Ion-Guide Isotope Separator On-Line (IGISOL) facility of  [48], the beam dump, He gas flow, the sextupole ion guide (SPIG), and the extractor electrodes [66].
A schematic diagram of the experimental setup consists of a target, the gas cell, the beam dump, the sextupole ion guide (SPIG), and the extractor electrodes shown in Fig. 1.The energetic MNT fragments produced from the target were traversed through a nickel(Ni) or havar window of the gas cell.Different configurations of the gas cells (Modified HIGISOL, MNT gas cell in A-and B-configuration) were used and tested in different experiments [48].The primary beam was stopped within a graphite beam-dump mounted either in front of the gas cell (modified HIGISOL and MNT gas cell in A-configuration) or after the gas cell (MNT gas cell in B-configuration) [48].The MNT products were stopped within the He buffer gas inside the gas cell.The gas flow subsequently extracted the thermalized ions from the gas cell, from which they were guided through a radiofrequency SPIG and extractor electrode system towards the mass separator [66].The target chamber was kept at +30 kV.The extracted ions were gradually accelerated towards the grounded electrostatic switchyard (SW), with typical voltage differences shown in Fig. 1 and mass separated using the dipole magnet having a mass resolving power (M/∆M), R ≈ 300, placed before the SW.Finally, in-beam α-decay spectra were measured using a Silicon (Si) detector mounted at the SW.
Four different experiments were performed to measure MNT residues between June 2019 -November 2021, as shown in Fig. 2. The characteristic α-peaks of 211 Bi, 211m Po, 211 Po, and 212m Po were clearly identified in addition to a minute amount of 211 At, 212m At, and 212 At.The dipole magnet setting was at mass, A = 211.The presence of α-peaks from the neighboring mass, A = 212, is due to a limited resolving power of the dipole magnet.As evident from Fig. 2, the relative production of dif- ferent α-emitting MNT products is found to be consistent across spectra, with 211 Bi as the dominant peak in all three measurements of 136 Xe+ 209 Bi reaction.However, the most intense αdecay peak of 211 Po (i.e., 7225 keV) was dominantly observed in the 136 Xe+ nat Pb reaction among all other peaks.This clearly reveals the relative enhanced production of 211 Po isomer over its ground-state in the 136 Xe+ nat Pb than the 136 Xe+ 209 Bi.It is important to bear in mind that the broader angular distributions of MNT fragments would result in a wider distribution of the stopping position of ions inside the gas cell [19].The wider distribution would cause a significant variation in extraction time, i.e., transport time from the gas cell to the SW (typically 100 ms).This leads to a larger uncertainty in the yields of 212m At (0.119 s) and 212 At (0.314 s) in addition to the lower statistics.Therefore, the estimation of IRs of 211 At is excluded.The IR of 211 Po was scrutinized against various experimental conditions such as: (i) different beam intensities, I (pnA); (ii) angular coverage of the gas cell window for the MNT products; (iii) He gas pressure within the gas cell, P (mbar); and have been tabulated in Table 1.Additionally, the carbon (C) catcher foils before the Si detector, the slit width opening at the electrostatic SW, and the thickness of the gas cell window, including the used material, would also affect the product yields and are, therefore, enlisted in Table 1.The isomeric yield (i.e., isomerto-ground state) ratio (IYR) of the 211 Po was deduced and normalized with the corresponding α-peak intensities.Therefore, the deduced IYR would be equivalent to the isomeric crosssection ratio (ICR), independent of experimental parameters such as manifested in Table 1 as well.Hence, IYR or ICR are referred to as IR in this letter.

Computations of spin distributions and IRs
A multidimensional dynamical approach based on Langevin equations has been adopted to examine the measured data for the 136 Xe+ 209 Bi/ nat Pb.The dynamical approach has adequately reproduced the mass, charge, energy, and angular distributions of the MNT-induced products for most of the limited studied reactions so far [18][19][20][21].The dynamical model was expanded to provide information about the spin distribution, thereby enabling the theoretical study of the spin distribution of MNT re-  211 Po, and the subsequently deduced isomeric ratio (IR) of 211 Po for a 945 MeV 136 Xe 31+ beam at different experimental conditions: intensity (I) of the beam, angular coverage (Ang.cov.) of the gas-cell window, pressure (P) of the He gas, thickness of carbon (C) foil placed before the Si detector, and slit width opening at the entrance to the electrostatic switchyard.The thickness of the entrance window foil of the gas cell was 4.3 mg/cm 2  (i) estimation of the spin distribution of an MNT product, and (ii) feeding of isomeric and ground states from the spin distribution.In the first step, the total angular momentum distribution was estimated by folding the orbital angular momentum brought in by the projectile with the non-zero intrinsic spin of the target.Moreover, the exchange of angular momentum due to the transfer of nucleons from projectile to target is necessary for the population of trans-target products, e.g., 211 Po, 211 Bi, etc., and was considered in the calculation.This was implemented as the sequential transfer of the nucleons.The spin of an excited MNT product is also affected by the evaporation of nucleons, although this effect was not included.
In the second step, the IR of 211 Po has been calculated by splitting the spin distribution into two parts: the lower spin distribution region is assumed to feed the ground-state (9/2 + ), and the higher-spin distribution to the isomeric state (25/2 + ).The spread in the spin distribution can be anticipated due to the evaporation of nucleons and the cascade of γ-decays from the MNT product.To account for these effects, an empirical systematic approach was applied for the calculation of IR using equation ( 1), consisting of an effective angular momentum cutoff J eff , and a spreading parameter ∆ [67], The Y (theory) J corresponds to the theoretical estimation of spin distribution for a particular MNT product, and sents the spin distribution associated with the ground-state (isomeric state).In our calculations, we assumed ∆ = 0.5, which is justified to account for the angular momentum carried away by the neutrons and γ rays [67][68][69].
In this work, the spin distribution of 211 Po was calculated for both reactions: 136 Xe+ 209 Bi at E/V B =1.12, 1.26, and 1.33; and 136 Xe+ nat Pb at E/V B =1.13, 1.27, and 1.34.Fig. 3(a) demonstrates the variation in the spin distributions of 211 Po for the two energies in both cases.It is found that the most probable value of spin distributions at near barrier energy (i.e., E/V B =1.12 and 1.13) is lower compared to the spin of the isomeric state of 211 Po (25/2 + ) as marked using a vertical line.However, the spin distributions for higher projectile energy (at E/V B =1.33 and 1.34) are significantly different for both reactions.The most probable value of the spin distribution obtained from 136 Xe+ nat Pb and 136 Xe+ 209 Bi is significantly larger and lower compared to the spin of 211 Po isomer, respectively.Variation in the spin distributions considering with and without the angular acceptance of an MNT gas cell can be seen in Fig. 3(b).Feeding of the spin distribution into the ground and isomeric states estimated from equations ( 1) and ( 2) is represented with a solid line for the angular acceptance 22 • -55 • for E/V B =1.33.

Discussions
The 209 Bi target differs from the nat Pb target in terms of relatively high ground-state spin of 209 Bi (9/2 − ) compared to almost zero spin of nat Pb (only 207 Pb, with 22.1% isotopic abundance, has a non-zero spin 1/2 − ).The ground-state spin of 211 Po has the identical spin as 209 Bi but with opposite parity (9/2 + ).Theory suggests that a larger production of high spin isomers is more probable in heavy-ion-induced MNT reactions due to the large angular momentum brought by projectiles compared to other conventional nuclear reaction processes.This is clearly endorsed by the observed α-spectra in which population of 211m Po, 212m At dominates over corresponding ground states.
As expected, one of the crucial observations reflected in Fig. 4(a) (shown with open symbols) is the IRs of 211 Po against various experimental parameters measured in the different experiments of 136 Xe+ 209 Bi and 136 Xe+ nat Pb.Different observations were found to be in excellent agreement.The final value of IR was determined by considering the weighted average (WAvg) of the measured IRs, shown with solid symbols.It should be stressed here that the IR of 211 Po for 136 Xe+ nat Pb is found to be ≈1.8 times higher in comparison to 136 Xe+ 209 Bi.Possible reasons for the different IR at an incident energy of 945 MeV are: (i) the intrinsic spin of the target, (ii) the angular momentum brought in by the projectile's momentum, and (iii) the number of transferred nucleons.It must be noted that the angular momentum brought in due to the momentum of 945 MeV 136 Xe beam in the formation of 211 Po from both reactions will be identical; however, coupling with the intrinsic spin of different targets could result in different spin values.
Different feasible production channels of 211 Po from 136 Xe+ nat Pb reaction would be 2p1n, 2p2n, 2p3n corresponding to dominant isotopic abundance of 208 Po (52.4%), 207 Po (22.1%), and 206 Po (24.1%).However, it is important to notice that production of 211 Po from the 2p2n, 2p3n channels would not only be suppressed by isotopic abundances but also from the significant reduction of MNT cross-sections with increasing number of transfer channels [19].Therefore, 2p2n channel would only be an effectively dominant route in the population of 211 Po.However, in case of 136 Xe+ 209 Bi, the production route 211 Po would be 2p1n channel.Moreover, it should be noted that the effect of 1n-transfer would be the same in both cases.Hence, 1p and 2p transfer can effectively be responsible for any significant variation in the production of 211 Po for both reactions.
A comparison of measured and computed IRs is represented in Fig. 4(b).The theoretical calculation of IRs at 12-13% above the barrier (i.e., IR<1) clearly indicates the smaller production of isomer compared to the ground state of 211 Po.Additionally, the IRs have similar values for both reactions despite the different spin of the targets and production routes.This means at near barrier energy, the coupling of the intrinsic spin of 209 Bi and the spin brought in by the projectile as well as the spin transferred to the 209 Bi by 1p-transfer is equivalent to the coupling of spin due to the projectile and spin transferred to the nat Pb by the 2p-transfer.However, the influence of the target spin on the production of MNT fragments will be more probable to appear at near-barrier energies due to the minimum amount of angular momentum that the projectile brings.Thus, the calculation implies a weak dependence of the spin distribution of 211 Po on the spin of 209 Bi and nat Pb targets at near-barrier energy.Moreover, target spin dependence on the spin distribution of an MNT fragment would hardly appear at higher projectile energies.
In figure 4(a) (solid symbols), the quantitative deduction of IRs at 945 MeV bombarding energy (i.e., IR>1) indicates that the isomer production of 211 Po significantly dominates over the ground state.The calculated IRs shown in Fig. 4(b) were found to increase with increasing projectile energy for both reactions.The increasing nature of IR can be understood as the projectile energy could bring in more angular momentum to the system via the projectile's momentum as well as the transfer of nucleons (in the case of MNT-induced reactions), indicating a large probability of the population of high spin states (i.e., isomers, in the present case) of MNT products and thereby resulting in higher values of IRs.The optimum angular range of the new gas cells was considered in the theoretical calculation to match the experimental and theoretical scenario.Finally, the weighted average (WAvg) of the estimated IRs was computed to simulate the production of the isomeric (25/2 + ) and ground (9/2 + ) states of 211 Po for the projectile energy loss within the targets.
It is evident from Fig. 4(b) that the population of 211 Po isomer over the ground state differs for the studied production routes, 136 Xe+ nat Pb and 136 Xe+ 209 Bi.Theoretical calculations (open squares) qualitatively explain the measured values.However, it underpredicts the experimental IRs by a factor of two for both reactions.Tentative assignment of (25/2 + ) of 211m Po might be one reason for the quantitative disagreement.The tentative assignment was made using empirical shell-model (ESM) calculations [70].Moreover, decay of the other two isomeric states (31/2 − ) and (43/2 + ) of 211 Po (tentatively assigned spin values) might change the independent production of ground (9/2 + ) and/or isomeric (25/2 + ) states, which could result in this  9 Be at 1 GeV/u in fragmentation process [73].
inconsistency.Additionally, as discussed in Sec. 3, the angular momentum of TLFs would not be just a sum of the ground-state spin of the target and the angular momentum transferred by projectiles and nucleon transfer.One must also consider the angular momentum carried away by nucleon evaporation from the excited MNT products, which would influence the final spin of the product.However, it was not considered in the calculations.More experimental data for different target-projectile systems would be helpful to properly incorporate its contribution in the theoretical calculation.Nonetheless, it is worth concluding that the p-transfer channels are strongly correlated with spin distributions and, thereby, the IRs.This means that more p-transfer could impart more spin to the MNT fragments and, therefore, more significant production of high spin state isomers.
Figure 5 exhibits a comparative study on the IRs of 211 Po deduced in the present work together with other experimental results over a wide range of projectile masses.The different shaded regions represent distinct nuclear reaction processes: (i) complete fusion (CF) process in α+ 208 Pb (solid square) [71]; (ii) incomplete fusion (ICF) process involved in 7 Li + 209 Bi (solid triangle) and 9 Be+ 208 Pb (solid square) [67]; and (iii) MNT reaction processes using 50 Ti+ 208 Pb (open square), 64 Ni+ 207 Pb (open square), 136 Xe+ nat Pb (solid square), 136 Xe+ 209 Bi (solid triangle) within 21-23% above barrier energies [36,72], and (iv) via fragmentation reaction process using 238 U+ 9 Be at 1 GeV/u (solid circle) [73].The IR of α+ 208 Pb and 9 Be+ 208 Pb at E/V B =1.21 were extrapolated from the increasing values of IRs reported at lower incident energies; one of them is shown with the open square at E/V B =1.06.However, an increment in the IRs and subsequent decrement may be anticipated with increasing projectile energies, similar to other reactions [74,75].Therefore, the reactions are essential to validate experimentally.Nonetheless, analysis endorses the increment of IRs populated from the 2p-channel compared to the 1p-channel.Anticipated IRs of 211 Po for several reactions were shown with an open dia-mond symbol.The 1p-and 2p-transfer channels were indicated with dash-dotted and dash-dot-dot lines, respectively.
The comparative analysis demonstrates that the IRs of 211 Po have primarily been affected by two entrance channel parameters: the projectile mass and the transfer channel production route.It is apparent that IRs of 211 Po gradually increase with the projectile mass, which reflects the sensitivity of spin distribution of the reaction products brought in by the mass of projectiles in different reaction processes (see Fig. 5).The ICF process is similar to transfer-like processes in which cluster transfer can be favored due to the weakly bound nature of projectiles, like 6,7 Li, 9 Be [76][77][78].In the ICF process, an enhanced angular momentum transfer has been observed in evaporation residues (ERs) compared to CF corresponding to the same production channels; e.g., α-transfer from 7 Li in ICF would impart more spin to ER compared to α particle CF [67].Similarly, in the present case, the residue produced from the MNT-induced reaction process via either 1p-or 2p-transfer channel can impart more angular momentum to the system than the one formed from the identical transfer of nucleons in the ICF process [67].This indicates that spin transferred via nucleon transfer strongly correlates with the projectile mass.Additionally, it is worth noticing the consistent enhancement of IRs for the 2p-transfer channel compared to the 1p-transfer channel over an extended mass region in distinct CF, ICF, and MNT reaction processes.
The IRs of 211 Po produced from 50 Ti+ 208 Pb and 64 Ni+ 207 Pb reactions were deduced from the α-spectra at relatively lower projectile energy, E/V B =1.06 and E/V B =0.21-1.20,respectively.The experiments were not aimed for the investigation of IRs [36,72].Significantly lower values of the IR were found for both reactions shown in Fig. 5.This might primarily be due to lower projectile energy or due to the limited angular coverage of the experimental setup (0 • ±2 • ) [47].The trend line obtained from the IRs of 211 Po from ICF and MNT processes predicts the large value of IRs for 50 Ti and 64 Ni projectiles at E/V B =1.21.Moreover, the IRs from 238 U+ 209 Bi/ nat Pb are predicted to be large compared to one obtained from 238 U+ 9 Be via fragmentation process.Hence, comparative analysis prompts the investigation of IRs for different target-projectile combinations populating 211 Po, including MNT reactions: 50 Ti+ 208 Pb, 64 Ni+ 207 Pb, and 238 U+ 208 Pb/ 209 Bi.Examining the aforementioned reactions at near-barrier energies would be worthwhile for the limpid perspicacity of the spin distributions.That is why exploring the 238 U+ 209 Bi/ 208 Pb/ 238 U reactions using the MNT approach is one of the prime objectives of an approved proposal to be performed soon at FRS-IC, GSI [79].

Summary
First measurement on the IRs of 211 Po was accomplished from the α-decay spectra produced via different channels of MNT reactions using 136 Xe+ 209 Bi and 136 Xe+ nat Pb.The population of isomers over the corresponding ground states was dominantly observed in different measurements of α-spectra.A dynamical approach based on Langevin equations was utilized to compute spin distributions of the MNT fragment for the first time and subsequently estimate the IRs at three distinct energies for both reactions.Close agreement between the computed IRs of 211 Po from 136 Xe+ 209 Bi and 136 Xe+ nat Pb reactions at nearbarrier energy indicate a weak dependence of target spin on the spin distribution and thereby would hardly affect the IRs at high energies, i.e., 26-34% above the barrier.Deduced IRs of 211 Po from 136 Xe+ nat Pb has been found to be increased by a factor of ≈1.8-times than obtained from 136 Xe+ 209 Bi.The considerable increment in 211 Po isomer can be attributed to the production route of the 2p-transfer channel in 136 Xe+ nat Pb compared to the 1p-transfer channel in 136 Xe+ 209 Bi.The estimated IRs were found to be strongly affected by projectile energy and qualitatively consistent with experimental findings of both reactions.However, theoretical estimations underpredict the measured IRs by a factor of two.
Comparative analysis on the IRs of 211 Po over the projectile mass in different nuclear reaction processes at E/V B ≈1.21-1.23 reveals two main entrance channel parameters: projectile mass and transfer channel production route, which strongly affect the IRs and, thereby, would play a major role in the spin distributions.The IRs of 211 Po has been found to be enhanced for the 2p-channel than for the 1p-channel over an extended mass range of the projectiles, inducing via CF, ICF, and MNT reaction processes.Present experimental and theoretical findings invoke for the comprehensive and systematic works to validate the predicted IRs for 9 Be+ 209 Bi, 7 Li+ 208 Pb, 50 Ti/ 64 Ni+ 208 Pb, 238 U+ 208 Pb/ 209 Bi including many other feasible systems above Coulomb barrier energies.

Figure 1 :
Figure 1: (Color online) A schematic diagram of the experimental arrangements consisting of a target, the MNT gas cell in B-configuration[48], the beam dump, He gas flow, the sextupole ion guide (SPIG), and the extractor electrodes[66].

Figure 3 :
Figure 3: (Color online) (a) Spin distribution of 211 Po using a dynamical model Langevin approach for 136 Xe+ 209 Bi at 12% (dotted line) and 33% (solid line) above the Coulomb barrier, and for 136 Xe+ nat Pb at 13% (dashed line) and 34% (dashed-dotted line) above barrier.(b) Unfolding of 211 Po into the ground and isomeric states corresponding to 22 • -55 • of angular coverage of gas cell window.The vertical line indicates the spin value of 211m Po (25/2 + ).

Figure 4 :
Figure 4: (Color online) (a) IRs of 211 Po produced in 136 Xe+ 209 Bi at E/V B =1.23±0.11and 136 Xe+ nat Pb at E/V B =1.21±0.12corresponding to 945 MeV beam energy in different experiments.Details of the experimental parameters are described in Table 1.(b) Estimation of IRs of 211 Po at three projectile energies and comparison of WAvg of IRs with measured results for 136 Xe+ 209 Bi and 136 Xe+ nat Pb.WAvg refers to the Weighted Average.Strip lines are shown as a guide to the eye for increasing IRs with projectile energy.
action products for the first time.The calculation of IR of a nuclide produced via MNT reaction can be conceptualized into two steps: