Impact of nuclear structure on the production and identification of superheavy nuclei

The shell structure of heavy nuclei with Z > 104, which can be produced in actinide-based complete fusion reactions, is studied with a modified two-center shell model. Using the macroscopic-microscopic approach, mass excesses and Qα-values are calculated and compared with available experimental data. The production cross sections of new superheavy nuclei decisively depend on the position of the proton shell closure.


Introduction
The experiments on complete fusion reactions with 48 Ca beam and various actinide targets were successfully carried out at FLNR (Dubna), GSI (Darmstadt), and LBNL (Berkeley) [1][2][3][4][5][6] in order to synthesize superheavy nuclei with Z = 112 − 118.The found experimental trend of the nuclear properties (Q α -values and half-lives) and cross sections of the superheavy elements (SHE) produced with 48 Ca-induced reactions reveals the increasing stability of nuclei approaching the spherical closed neutron shell N = 184, and also indicates a relatively small effect of the proton shell at Z = 114 [7,8].With the microscopic-macroscopic models [9][10][11][12] "the island of stability" of the SHE is predicted at charge number Z = 114 and neutron number N = 184.In accordance with predictions of the relativistic and nonrelativistic mean field models [13][14][15], the most stable nuclei have Z = 120 − 126 and N = 184.If this is true, then there is a hope to synthesize new SHE with Z ≥ 119 by using the present experimental set-ups and actinide-based reactions with neutron-rich stable projectiles heavier than 48 Ca.

Modified microscopic-macroscopic approach
The stability of superheavies is related to the shell effects which are ruled by the mean field and the spin-orbit interaction.In Ref. [16] we proposed a microscopic-macroscopic approach based on the two-center shell model (TCSM) [17].The parameters were set so to describe in the best way the spins and parities of the ground state of heavy nuclei.With this modified microscopic-macroscopic approach one can reveal the trends in the shell effects and Q α values with Z.Note that the global fit is out of our task and the obtained binding energies are the subject of further improvement.
Besides our results, the microscopic-macroscopic models [9][10][11][12] as well as the phenomenological model [18] provide us the Q values of the reactions, fission barriers and neutron separation energies of a e-mail: antonenk@theor.jinr.ru on N [19] in comparison with the predictions of Refs.[9,18].As follows, for the compound nuclei with Z = 120 − 124 we expect larger survival probabilities than for the nuclei with Z = 114.As seen in Fig. 1, the calculated Q α are in a good, within 0.3 MeV, agreement with the available experimental data.The shell at N = 162 is less pronounced in our calculations than in Refs.[9][10][11][12] The shell effects at Z = 114 and N = 172 − 176 provide rather weak dependence of Q α on N. The strong role of the shell at Z = 120 and N = 184 is reflected in the well pronounced minimum of Q α .As in our calculations, there is strong evidence of the shell closure at N = 184 in the phenomenological model [18].To shed light on the dependence of the level density on the shell effects, the calculated energy dependencies of the level densities [20] are fitted by the well-known expression of the Fermi-gas model.Then we obtain the dependence of the level density parameter a on Z, N, and excitation energy.We consider the dependencies of a on Z (Fig. 2) for three α-decay chains containing the nuclei 296,298,300 120 which could be synthesized with available projectiles and targets.At Z = 108 and 120 there are minima of a in all chains.This reflects quite a strong proton shell effects at Z = 108 and 120.At Z = 120, the minima of a are the deepest and well pronounced.The similar behavior of a occurs near Z = 82.As in Ref. [19], we conclude here that the modified TCSM provides the proton shell closure at Z = 120.The sub-shell at Z = 114 exists but provides weaker shell effect than at Z = 120.For nuclei with Z = 124 − 128, the minima of a are due to the neutron shell at N = 184.
Using our predictions of nuclear properties [19], we calculated the values of σ ER in the reactions 48 Ca, 50 Ti, 54 Cr, 58 Fe, 64 Ni+ 238 U, 244 Pu, 248 Cm, 249 Cf (Fig. 3).In comparison to our previous calculations with the mass table of Ref. [9], in Fig. 3  larger values of σ ER .A good description of existing data allows us to be confident in the predictions for the reactions with heavier projectiles.With 50 Ti beam the values of σ ER for the nuclei with Z = 114 − 118 are expected to be 5-10 times smaller than those resulting for 48 Ca beam.The main reason for this is the decrease of fusion probability with mass asymmetry in the entrance channel of reaction.With 50 Ti the nucleus 295 120 is predicted to be produced with the cross section of 23 fb.In the 54 Cr+ 248 Cm reaction the compound nucleus would have 3 neutrons more than in the 50 Ti+ 249 Cf reaction.Therefore, the decrease of fusion probability is partly compensated by the increase of survival probability and the nucleus 298 120 could INPC 2013 be produced with the cross section of 10 fb.For the production of nuclei with Z = 122 − 126, 64 Ni beam would lead to larger cross sections, 1-8 fb.

Summary
The calculations performed with the modified TCSM reveal quite strong shell effects at Z = 120 − 126 and N = 184 as in the self-consistent mean-field treatments.If our prediction of the structure of heaviest nuclei is correct, than one can expect the production of evaporation residues Z = 120 in the reactions 50

DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences, are necessary to calculate evaporation residue cross sections σ ER .The value of survival probability strongly depends on B f − B n , the difference between the height B f of the fission barrier and the neutron separation energy B n .The values of B n predicted with different models vary within 0.5 MeV and the shell effects or B f cause the main difference in the dependencies of B f − B n

Figure 2 .
Figure 2. Calculated parameter of level density as a function of Z for nuclei of alpha-decay chains containing 296,298,300 120.Neutron numbers are given at the corresponding data points.

Figure 3 .
Figure 3. evaporation residue cross sections in the maxima of excitation functions versus charge number Z for the reactions 48 Ca, 50 Ti, 54 Cr, 58 Fe, 64 Ni+ 238 U, 244 Pu, 248 Cm, 249 Cf.The excitation energies of compound nuclei are given in brackets.
Ti+ 249 Cf and 54 Cr+ 248 Cm with the cross sections 23 and 10 fb, respectively.The Z = 120 nuclei with N = 175 − 179 are expected to have Q α about 12.1-11.2MeV and lifetimes 1.7 ms-0.16s in accordance with our predictions.The experimental measurement of Q α for at least one isotope of Z = 120 would help us to set proper shell gaps in the region of SHE.This work was supported in part by RFBR.The IN2P3 (France)-JINR (Dubna), and Polish -JINR (Dubna) Cooperation Programmes are gratefully acknowledged.