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Synthesizing the new superheavy elements has obtained lots of attention from the theorists and experimentalists in the nuclear physics field since the "island of stability" of superheavy nuclei(SHN) has been proposed by the shell model in the 1960s[1]. The superheavy nuclei contain hundreds of nucleons and have been considered as a natural laboratory used to investigate the many body problems and structure of atomic under a strong Coulomb force field. Currently, the experiments of synthesis superheavy nuclei cost an amount of money and have a long experimental period, because of the extremely low synthesis cross section of new superheavy elements. Therefore, before performing such experiments, it is necessary to make theoretical predictions for specific nuclei with the best projectile-target combinations and incident energy, formation cross-section, and evaporation channels.
On the experimental side, the fifteen superheavy elements (Z = 104~118) have been synthesized based on the hot-fusion and cold-fusion reactions at the laboratories in the past decades[2]. Based on the hot-fusion reactions, the elements of rutherfordium, dubnium, seaborgium, flerovium, moscovium, livermorium, tennessine and oganesson have been synthesized firstly. The element of rutherfordium (Rf, Z = 104) is essentially discovered simultaneously in Dubna[3] and Berkeley[4] in the reactions
$ ^{249}{\rm{Cf}} $ ($ ^{12, 13}{\rm{C}} $ , 3~4n)$^{257,\, 258,\, 259}{\rm{Rf}}$ . The element of dubium (Db, Z = 105) is essentially produced simultaneously in Dubna[5] and Berkeley[6] in$ ^{249}{\rm{Cf}} $ ($ ^{15}{\rm{N}} $ , 4n)$ ^{260}{\rm{Db}} $ and$ ^{243}{\rm{Am}} $ ($ ^{22}{\rm{Ne}} $ , 4n)$ ^{261}{\rm{Db}} $ . The element of seaborgium (Sg, Z = 106) is essentially discovered at Berkeley[7] in$ ^{249}{\rm{Cf}} $ ($ ^{18}{\rm{O}} $ , 4n)$ ^{263}{\rm{Sg}} $ . The element of flerovium (Fl, Z = 114) is discovered at Dubna[8] in$ ^{244}{\rm{Pu}} $ ($ ^{48}{\rm{Ca}} $ , 3~6n)$ ^{286-289}{\rm{Fl}} $ . The element of moscovium (Mc, Z = 115) is syntheiszed at Dubna[9]$ ^{243}{\rm{Am}} $ ($ ^{48}{\rm{Ca}} $ , 3n)$ ^{288}{\rm{Mc}} $ . The element of livermoriu (Lv, Z = 116) is produced at Dubna[10] in$ ^{245}{\rm{Cm}} $ ($ ^{48}{\rm{Ca}} $ , xn)$ ^{293-x}{\rm{Fl}} $ . The element of tennessine (Ts, Z = 117) is discovered at Dubna[11] in$ ^{249}{\rm{Bk}} $ ($ ^{48}{\rm{Ca}} $ , 3-4n)$ ^{293-294}{\rm{Fl}} $ . The element of oganesson (Og, Z = 118) is syntheiszed at Dubna[12] in$ ^{249}{\rm{Cf}} $ ($ ^{48}{\rm{Ca}} $ , 3n)$ ^{294}{\rm{Og}} $ . Based on the cold-fusion reactions, the elements of seaborgium, bohrium, hassium, meitnerium, darmstadtium, roentgenium, copernicium and nihonium have been synthesized firstly. The element of seaborgium (Sg, Z = 106) is essentially discovered at Dubna[13] in the reactions of$ ^{207}{\rm{Pb}} $ ($ ^{54}{\rm{Cr}} $ , 2n)$ ^{259}{\rm{Sg}} $ . The element of bohriumium (Bh, Z = 107) is produced at GSI[14] in$ ^{209}{\rm{Bi}} $ ($ ^{54}{\rm{Cr}} $ , 1n)$ ^{262}{\rm{Bh}} $ . The element of hassium (Hs, Z = 108) is essentially syntheiszed at GSI[15] in$ ^{208}{\rm{Pb}} $ ($ ^{58}{\rm{Fe}} $ , 2n)$ ^{265}{\rm{Hs}} $ . The element of meitnerium (Mt, Z = 109) is essentially discovered at GSI[16] in$ ^{209}{\rm{Bi}} $ ($ ^{58}{\rm{Fe}} $ , 1n)$ ^{266}{\rm{Mt}} $ . The element of darmstadtium (Ds, Z = 110) is essentially produced at GSI[17] in$ ^{208}{\rm{Pb}} $ ($ ^{62}{\rm{Ni}} $ , 1n)$ ^{269}{\rm{Ds}} $ . The element of roentgenium (Rg, Z = 111) is essentially discovered at GSI[18] in$ ^{209}{\rm{Bi}} $ ($ ^{64}{\rm{Ni}} $ , 1n)$ ^{272}{\rm{Rg}} $ . The element of copernium (Cn, Z = 112) is essentially syntheiszed at GSI[19] in$ ^{208} {\rm{Pb}}$ ($ ^{70}{\rm{Zn}} $ , 1n)$ ^{277}{\rm{Rg}} $ . The element of nihonium (Nh, Z = 113) is essentially produced at RIKEN[20] in$ ^{209}{\rm{Bi}} $ ($ ^{70}{\rm{Zn}} $ , 1n)$ ^{278}{\rm{Nh}} $ . The earliest synthesis of superheavy elements with Z = 104~118 are illustrated in Table 1 as elements, reactions, evaporation channel(E.C.), incident energy, isotope number, laboratory and year. In IMP Lanzhou, the superheavy isotopes of$^{258, \,259}{\rm{Db}}$ [21],$^{264, \,265,\, 266}{\rm{Bh}}$ [22] and$ ^{271}{\rm{Ds}} $ [23] have been synthesized.SHN Reactions E.C. Energies I.N. Lab. Year Rf (104) $ ^{12}{\rm{C}} $ + $ ^{249}{\rm{Cf}} $ xn[3] 125 MeV 13 Dubna 1969 $ ^{13}{\rm{C}} $ + $ ^{249}{\rm{Cf}} $ xn[4] 135 MeV Berkeley 1969 Db (105) $ ^{15}{\rm{N}} $ + $ ^{249}{\rm{Cf}} $ 4n [6] 85 MeV 11 Berkeley 1970 $ ^{22}{\rm{Ne}} $ + $ ^{243}{\rm{Am}} $ 4n[5] 114 MeV Dubna 1970 Sg (106) $ ^{54}{\rm{Cr}} $ + $ ^{207}{\rm{Pb}} $ 2n[13] 262 MeV 12 Dubna 1974 $ ^{18}{\rm{O}} $ + $ ^{249}{\rm{Cf}} $ 4n[7] 95 MeV Berkeley 1974 Bh (107) $ ^{54}{\rm{Cr}} $ + $ ^{209}{\rm{Bi}} $ 1n[14] 262 MeV 10 GSI 1981 Hs (108) $ ^{58}{\rm{Fe}} $ + $ ^{208}{\rm{Pb}} $ 2n[15] 291 MeV 12 GSI 1984 Mt (109) $ ^{58}{\rm{Fe}} $ + $ ^{209}{\rm{Bi}} $ 1n[16] 299 MeV 7 GSI 1982 Ds (110) $ ^{62}{\rm{Ni}} $ + $ ^{208}{\rm{Pb}} $ 1n[17] 311 MeV 8 GSI 1985 Rg (111) $ ^{64}{\rm{Ni}} $ + $ ^{209}{\rm{Bi}} $ 1n[18] 318, 320 MeV 7 GSI 1995 Cn (112) $ ^{70}{\rm{Zn}} $ + $ ^{208}{\rm{Pb}} $ 1n[19] 344 MeV 6 GSI 1996 Nh (113) $ ^{70}{\rm{Zn}} $ + $ ^{209}{\rm{Bi}} $ 1n[20] 352.6 MeV 6 RIKEN 2004 Fl (114) $ ^{48}{\rm{Ca}} $ + $ ^{244}{\rm{Pu}} $ xn[8] 352.6 MeV 5 Dubna 2004 Mc (115) $ ^{48}{\rm{Ca}} $ + $ ^{243}{\rm{Am}} $ 3n[9] 248, 253 MeV 4 Dubna 2004 Lv (116) $ ^{48}{\rm{Ca}} $ + $ ^{245}{\rm{Cm}} $ xn[10] 243 MeV 4 Dubna 2004 Ts (117) $ ^{48}{\rm{Ca}} $ + $ ^{249}{\rm{Bk}} $ xn[11] 247, 252 MeV 2 Dubna 2011 Og (118) $ ^{48}{\rm{Ca}} $ + $ ^{249}{\rm{Cf}} $ 3n[12] 251 MeV 1 Dubna 2006 Table 1. The initial synthesized superheavy elements with atomic number Z=104~118 were illustrated as the produced method, reactions, incident energy, isotope number(I.N.), laboratories, year and reference.
On the theoretical side, some sophisticated and practical theory models such as the time-dependent Hartree-Fock(TDHF)[24-26], the improved quantum molecular dynamics(ImQMD) model[27-29], the dynamical approach based on Langevin equations[30-31], the dinuclear system model(DNS)[32-36] have been developed to describe the synthesis mechanisms of superheavy nuclei and predict their synthesis cross sections. The DNS model has been adapted which better involves the shell effect, dynamical deformation, fission, quasi-fission, deep-inelastic and odd-even effect. The DNS model has reproduced the excitation functions of the evaporation channels for the available experimental results in the Refs. [32-33, 36-37].
In this work, we have calculated all possible combinations of projectile-target for synthesizing the new superheavy elements Z = 119, 120 within the DNS model. The aim of this paper is to investigate the influence of the entrance channel and projectile isospin on the production cross-sections of new superheavy elements in fusion-evaporation reactions and to predict the synthesis cross-section of new SHEs with Z = 119, 120. The article was organized as follows: In Sec. 2 we give a brief description of the DNS model. Calculation results and discussions are presented in Sec. 3. The summary is concluded in Sec. 4.
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In previous work, the DNS model provides the calculations of the superheavy nuclei that have a good agreement with the available experimental data[32-33, 38-39, 56-75], which has been used to predict production cross sections of the unknown SHEs located at the next periodic table of elements, based on the reactions of combinations of stable projectile-target. In this paper, we have performed systematic calculations of all possible combinations of available projectile-target particularly involving radioactive nuclei. The calculation results and details for the reactions of
$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ,$ ^{56}{\rm{Mn}} $ +$ ^{243}{\rm{Am}} $ ,$ ^{68}{\rm{Zn}} $ +$ ^{232}{\rm{Th}} $ ,$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ are introduced as following graphs. All possible combinations of projectile-target have been demonstrated in Table 2, which have a long enough life to collide. The cross sections of 2n-, 3n-, 4n-, and 5n-evaporation channels for the reactions of the projectile from Ca to Zn bombarding on target from Ac to Fm have been exhibited in Table 3. From the calculation results, we found that the projectile beyond the Ni-induced reaction provides an extremely low cross section for the new superheavy elements with Z = 119, 120. Therefore, the discussion has been made for the reactions of$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ and$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ at wide excitation energy.T.$ \backslash $ P. $ ^{40-48}{\rm{Ca}} $ $ ^{43-49}{\rm{Sc}} $ $ ^{44-50}{\rm{Ti}} $ $ ^{47-51}{\rm{V}} $ $ ^{50-54}{\rm{Cr}} $ $ ^{51-56}{\rm{Mn}} $ $ ^{53-60}{\rm{Fe}} $ $ ^{56-61}{\rm{Co}} $ $ ^{58-64}{\rm{Ni}} $ $ ^{63-65}{\rm{Cu}} $ $ ^{64-68}{\rm{Zn}} $ $ ^{232}{\rm{Th}} $ $ ^{272-280}{\rm{Ds}} $ $ ^{275-281}{\rm{Rg}} $ $ ^{276-282}{\rm{Cn}} $ $ ^{279-283}{\rm{Nh}} $ $ ^{282-286}{\rm{FI}} $ $ ^{283-288}{\rm{Mc}} $ $ ^{285-292}{\rm{Lv}} $ $ ^{288-293}{\rm{Ts}} $ $ ^{290-296}{\rm{Og}} $ $ ^{295-297}{\rm{119}} $ $ ^{296-300}{\rm{120}} $ $ ^{231}{\rm{Pa}} $ $ ^{271-279}{\rm{Rg}} $ $ ^{274-280}{\rm{Cn}} $ $ ^{275-281}{\rm{Nh}} $ $ ^{278-282}{\rm{FI}} $ $ ^{281-285}{\rm{Mc}} $ $ ^{282-287}{\rm{Lv}} $ $ ^{284-291}{\rm{Ts}} $ $ ^{287-291}{\rm{Og}} $ $ ^{289-295}{\rm{119}} $ $ ^{294-296}{\rm{120}} $ $ ^{295-299}{\rm{121}} $ $ ^{238}{\rm{U}} $ $ ^{278-286}{\rm{Cn}} $ $ ^{281-287}{\rm{Nh}} $ $ ^{282-288}{\rm{FI}} $ $ ^{285-289}{\rm{Mc}} $ $ ^{288-292}{\rm{Lv}} $ $ ^{289-294}{\rm{Ts}} $ $ ^{291-298}{\rm{Og}} $ $ ^{294-298}{\rm{119}} $ $ ^{296-303}{\rm{120}} $ $ ^{301-303}{\rm{121}} $ $ ^{302-306}{\rm{122}} $ $ ^{237}{\rm{Np}} $ $ ^{277-285}{\rm{Nh}} $ $ ^{280-286}{\rm{FI}} $ $ ^{281-287}{\rm{Mc}} $ $ ^{284-288}{\rm{Lv}} $ $ ^{287-291}{\rm{Ts}} $ $ ^{288-293}{\rm{Og}} $ $ ^{290-297}{\rm{119}} $ $ ^{293-297}{\rm{120}} $ $ ^{295-301}{\rm{121}} $ $ ^{300-302}{\rm{122}} $ $ ^{301-305}{\rm{123}} $ $ ^{244}{\rm{Pu}} $ $ ^{284-292}{\rm{FI}} $ $ ^{287-293}{\rm{Mc}} $ $ ^{288-294}{\rm{Lv}} $ $ ^{291-295}{\rm{Ts}} $ $ ^{294-298}{\rm{Og}} $ $ ^{295-300}{\rm{119}} $ $ ^{297-304}{\rm{120}} $ $ ^{300-304}{\rm{121}} $ $ ^{302-308}{\rm{122}} $ $ ^{307-309}{\rm{123}} $ $ ^{308-312}{\rm{124}} $ $ ^{243}{\rm{Am}} $ $ ^{283-291}{\rm{Mc}} $ $ ^{286-292}{\rm{Lv}} $ $ ^{287-293}{\rm{Ts}} $ $ ^{290-294}{\rm{Og}} $ $ ^{293-297}{\rm{119}} $ $ ^{294-299}{\rm{120}} $ $ ^{296-303}{\rm{121}} $ $ ^{299-303}{\rm{122}} $ $ ^{301-307}{\rm{123}} $ $ ^{306-308}{\rm{124}} $ $ ^{307-311}{\rm{125}} $ $ ^{247}{\rm{Cm}} $ $ ^{287-295}{\rm{Lv}} $ $ ^{290-296}{\rm{Ts}} $ $ ^{291-297}{\rm{Og}} $ $ ^{294-298}{\rm{119}} $ $ ^{297-301}{\rm{120}} $ $ ^{298-303}{\rm{121}} $ $ ^{300-307}{\rm{122}} $ $ ^{303-307}{\rm{123}} $ $ ^{305-311}{\rm{124}} $ $ ^{310-312}{\rm{125}} $ $ ^{311-315}{\rm{126}} $ $ ^{247}{\rm{Bk}} $ $ ^{287-295}{\rm{Ts}} $ $ ^{290-296}{\rm{Og}} $ $ ^{291-297}{\rm{119}} $ $ ^{294-298}{\rm{120}} $ $ ^{297-301}{\rm{121}} $ $ ^{298-303}{\rm{122}} $ $ ^{300-307}{\rm{123}} $ $ ^{303-307}{\rm{124}} $ $ ^{305-311}{\rm{125}} $ $ ^{310-312}{\rm{126}} $ $ ^{311-315}{\rm{127}} $ $ ^{251}{\rm{Cf}} $ $ ^{291-299}{\rm{Og}} $ $ ^{294-300}{\rm{119}} $ $ ^{295-301}{\rm{120}} $ $ ^{298-302}{\rm{121}} $ $ ^{301-305}{\rm{122}} $ $ ^{302-307}{\rm{123}} $ $ ^{304-311}{\rm{124}} $ $ ^{307-311}{\rm{125}} $ $ ^{309-315}{\rm{126}} $ $ ^{314-316}{\rm{127}} $ $ ^{315-319}{\rm{128}} $ $ ^{252}{\rm{Es}} $ $ ^{292-300}{\rm{119}} $ $ ^{295-301}{\rm{120}} $ $ ^{296-302}{\rm{121}} $ $ ^{299-303}{\rm{122}} $ $ ^{302-306}{\rm{123}} $ $ ^{303-308}{\rm{124}} $ $ ^{305-312}{\rm{125}} $ $ ^{308-312}{\rm{126}} $ $ ^{310-316}{\rm{127}} $ $ ^{315-317}{\rm{128}} $ $ ^{316-320}{\rm{129}} $ $ ^{257}{\rm{Fm}} $ $ ^{297-305}{\rm{120}} $ $ ^{300-306}{\rm{121}} $ $ ^{301-307}{\rm{122}} $ $ ^{304-308}{\rm{123}} $ $ ^{307-311}{\rm{124}} $ $ ^{308-313}{\rm{125}} $ $ ^{310-317}{\rm{126}} $ $ ^{313-317}{\rm{127}} $ $ ^{315-321}{\rm{128}} $ $ ^{320-322}{\rm{129}} $ $ ^{321-325}{\rm{130}} $ Table 2. The possible combinations of projectiles-targets for synthesizing new superheavy nuclei.
Rreaction E.C. $ E^* $ $ \sigma $ /pb Reaction E.C. $ E^* $ $ \sigma $ /pb $ ^{48} {\rm{Ca}} $+$ ^{252}{\rm{Es}} $ 2n 34 5.4×10−3 $ ^{48} {\rm{Ca}} $+$ ^{257}{\rm{Fm}} $ 2n 36 1×10−3 3n 34 0.3 3n 38 8.4×10−3 4n 40 0.07 4n 42 0.01 5n 50 0.03 5n 52 5.5×10−3 $ ^{49} {\rm{Sc}} $+$ ^{251}{\rm{Cf}} $ 2n 34 0.01 $ ^{49} {\rm{Sc}} $+$ ^{252}{\rm{Es}} $ 2n 36 9×10−4 3n 34 0.5 3n 38 0.01 4n 40 0.1 4n 44 4.4×10−3 5n 50 0.04 5n 56 7.4×10−4 $ ^{46} {\rm{Ti}} $+$ ^{247}{\rm{Bk}} $ 2n 30 4.3 $ ^{50} {\rm{Ti}} $+$ ^{251}{\rm{Cf}} $ 2n 34 8.7×10−4 3n 36 0.7 3n 36 0.01 4n 48 0.07 4n 44 3.7×10−3 5n 64 1×10−3 5n 56 6×10−4 $ ^{51} {\rm{V}} $+$ ^{247}{\rm{Cm}} $ 2n 34 0.04 $ ^{51} {\rm{V}} $+$ ^{247}{\rm{Bk}} $ 2n 34 1.8×10−3 3n 36 0.08 3n 38 5.4×10−3 4n 42 0.1 4n 48 2.2×10−3 5n 50 0.01 5n 62 2.5×10−4 $ ^{54} {\rm{Cr}} $+$ ^{243}{\rm{Am}} $ 2n 30 5×10−3 $ ^{54} {\rm{Cr}} $+$ ^{247}{\rm{Cm}} $ 2n 38 4×10−4 3n 34 0.01 3n 38 2.8×10−4 4n 44 6×10−3 4n 46 5×10−3 5n 56 2.5×10−4 5n 56 9×10−6 $ ^{56} {\rm{Mn}} $+$ ^{244}{\rm{Pu}} $ 2n 32 6×10−4 $ ^{56} {\rm{Mn}} $+$ ^{243}{\rm{Am}} $ 2n 36 3.6×10−5 3n 34 0.03 3n 38 2×10−4 4n 40 5.3×10−3 4n 46 1.2×10−4 5n 50 2.6×10−3 5n 58 2.7×10−5 $ ^{60} {\rm{Fe}} $+$ ^{237}{\rm{Np}} $ 2n 32 1.4×10−3 $ ^{60} {\rm{Fe}} $+$ ^{244}{\rm{Pu}} $ 2n 36 8×10−6 3n 34 3×10−3 3n 40 5.4×10−5 4n 44 2.1×10−3 4n 48 3×10−5 5n 56 1×10−4 5n 50 5×10−5 $ ^{61} {\rm{Co}} $+$ ^{238}{\rm{U}} $ 2n 34 2.7×10−4 $ ^{61} {\rm{Co}} $+$ ^{237}{\rm{Np}} $ 2n 36 1.5×10−5 3n 36 6.6×10−4 3n 40 4.4×10−5 4n 46 1.6×10−3 4n 50 4.5×10−5 5n 52 2.8×10−4 5n 60 1×10−5 $ ^{64} {\rm{Ni}} $+$ ^{231}{\rm{Pa}} $ 2n 36 < 10−6 $ ^{64} {\rm{Ni}} $+$ ^{238}{\rm{U}} $ 2n 36 < 10−6 3n 38 < 10−6 3n 38 < 10−6 4n 42 < 10−6 4n 42 < 10−6 5n 50 < 10−6 5n 50 < 10−6 $ ^{65} {\rm{Cu}} $+$ ^{232}{\rm{Th}} $ 2n 36 0.08 $ ^{65} {\rm{Cu}} $+$ ^{231}{\rm{Pa}} $ 2n 20 < 10−6 3n 38 < 10−6 3n 20 < 10−6 4n 42 < 10−6 4n 20 < 10−6 5n 50 < 10−6 5n 20 < 10−6 $ ^{68} {\rm{Zn}} $+$ ^{232}{\rm{Ac}} $ 2n 20 < 10−6 $ ^{68} {\rm{Zn}} $+$ ^{232}{\rm{Th}} $ 2n 20 < 10−6 3n 38 < 10−6 3n 20 < 10−6 4n 42 < 10−6 4n 20 < 10−6 5n 50 < 10−6 5n 20 < 10−6 Table 3. The production mechanisms of new superheavy nuclei with Z = 119, 120 are listed as reactions, evaporation channels, excitation energy, and cross sections.
To investigate the effect of the entrance channel on the colliding process, the interaction potential along distance, the sticking time along with angular momentum, and internal excitation energies are listed in Fig. 1, where the black solid lines stand for the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ($ \eta $ =0.68), dash red lines stand for the reactions$ ^{56}{\rm{Mn}} $ +$ ^{243}{\rm{Am}} $ ($ \eta $ =0.62), and the dash-dot blue lines stand for the reaction$ ^{68}{\rm{Zn}} $ +$ ^{232}{\rm{Th}} $ ($ \eta $ =0.54). The$ \eta $ is the mass asymmetry with respect to the$\eta = (A_{\rm T}-A_{\rm P})/(A_{\rm T}+A_{\rm P})$ where the$A_{\rm T}$ and$A_{\rm P}$ are the mass of the target and projectile, respectively. Panel (a) shows the interaction potential energy of the different combinations that lead to the same element being so different, which is due to the collisions with the smaller$ \eta $ lead to the larger Coulomb force. Panel (b) shows that the sticking time varies along with the angular momentum, which has been calculated by the parametrization deflection function. The parametrization deflection function is highly dependent on the interaction potential. It is found that the collisions with deep pocket potential have a long sticking time. For given impact parameter$ L $ = 10$ \hbar $ , internal excitation energies evolve with time, which accumulates from kinetic energy dissipation. The internal excitation energy reaches the equilibrium state at the time about 2$ \times 10^{-22} $ s. At the equilibrium states, the collisions with large$ \eta $ own the large internal excitation energy which is related to the interaction potential or the structure of colliding partners. The interaction potential, and sticking time are basic input physic quantities in the DNS model. The internal excitation energy could reveal the dynamic diffusion process.Figure 1. The black solid lines, red dash lines, and blue dash-dot lines stand for the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ,$ ^{56}{\rm{Mn}} $ +$ ^{243}{\rm{Am}} $ ,$ ^{68}{\rm{Zn}} $ +$ ^{232}{\rm{Th}} $ , respectively. Panel (a) shows interaction potential along with the distance. The panel (b) represents the sticking time to angular momentum (A. M.) at the incident energy$ E_{\rm lab} $ = 1.1$ V_{\rm B} $ . Panel (c) displays the internal excitation energy along with time for the given A. M. 10$ \hbar $ . (color online)In the DNS model, the colliding partners overcome the Coulomb barrier to form the composite system, where the relative kinetic energy and angular momentum dissipated into the internal excitation energy which enables the nucleons to transfer between the touching projectile and target. The probability of nucleon transfer is calculated by solving a set of master equations in which the PES or the driving potential is the crucial input physical quantity. The PES is derived by Eq. (15) which contained the ground state Q value, the interaction potential, and the rotational energy at the head-on collision with the fixed distance. The driving potential and PES of the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ($ \eta $ =0.68),$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ($ \eta $ =0.66),$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ ($ \eta $ =0.63) lead to the new element with atomic number Z=119 are listed in Fig. 2 as the three lists of panels. The up-panels and bottom panels are the driving potential and PES, respectively. In the up-panels, the arrow lines and the bottom dash lines stand for the injection points. The up dash lines represent the Businaro-Gallone (B.G.) points. The barrier from the injection point to the B.G. point was named the inner fusion barrier. The inner barriers ($ B_{\rm if} $ ) of the$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ($ \eta $ =0.68),$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ($ \eta $ =0.66),$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ ($ \eta $ =0.63) are 13.6 MeV, 12.9 MeV, 13.8 MeV. It is found that the reaction of$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ($ \eta $ =0.66) own the smaller inner fusion barrier, which might result in the large fusion probability. The open stars stand for the injection points and compound nuclei in the bottom panels where the valley trajectories as the solid black lines are added. We could see that the injection points are located along with the driving potential which is close to the$ \beta $ -stable line. There is a big pocket in the symmetry region of the PES. The PESs might clearly show the paths of the colliding system diffusion.Figure 2. The driving potential and potential energy surface of the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ are shown as the up-panels and bottom-panels, respectively. (color online)Fig. 3 shows three lists of panels from left to right that are the driving potential and PES of the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ($ \eta $ =0.68),$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ($ \eta $ =0.66),$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ ($ \eta $ =0.64) at the head-on collision orientation with the frozen distance, respectively, which has similar content to the Fig. 2. The up-panels present the inner fusion barriers$(B_{\rm if} )$ of$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ($ \eta $ =0.68),$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ($ \eta $ =0.66),$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ ($ \eta $ =0.64) own the values 13.4, 15.2, 16.4 MeV respectively. It is found that the inner fusion barrier increases with the decreased mass asymmetry system, which could be used to evaluate the relative fusion probability. Compared to the colliding systems used to produce new element Z = 119, the inner barriers of the colliding system for synthesizing new element Z = 120 have a larger value, which means that element Z = 120 has a lower production cross-section than that of element Z = 119. The bottom panels (d), (e) and (f) exhibit the PESs which could be applied to predict the tendency of probability diffusion.Figure 3. The driving potential and potential energy surface(PES) of the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ are shown as the up-panels and bottom-panels, respectively. (color online)The DSN model classifies the fusion-evaporation reactions into three stages i.e. the capture stage, the fusion stage, and the survival stage, which was calculated based on one dimension barrier penetration model or the Hill-Wheeler formula (Eq. 3), master equation and evaporation statistics model, respectively, corresponding to the three lists of panels from the left to right in Fig. 4, where the projectile
$ ^{48}{\rm{Ca}} $ ,$ ^{50}{\rm{Ti}} $ and$ ^{54}{\rm{Cr}} $ induced reactions are marked by red dash lines, blue dash-dot lines, and black solid lines, respectively. The up-panels are for the reactions of$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ leading to the new superheavy element Z=119. The capture cross-section of the head-on collisions of$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ are listed in panel (a). It is found that the penetration probability in descending order is$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ ,$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ in the sub-barrier region, which do not respect to their mass asymmetry order. Because the deformation of colliding partners coupled with the Coulomb force plays a crucial role in the penetration process. Panel (b) shows the fusion probability from top to bottom where the reactions$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ , respectively, which has consistency with the inner fusion barrier order. In the framework of the DNS model, complete fusion reactions are treated as all the nucleons transferred from the projectile to the target. In the diffusion process, the formation probability of all possible fragments is evaluated by solving a set of master equations. The fragments reaching the B.G. point would be considered as overcoming the inner fusion barrier, which is deemed as the fusion event. The reactions$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ lead to the excited compound nuclei$ ^{300}{\rm{119}} $ ,$ ^{297}{\rm{119}} $ , respectively, whose survival probability of 2n-, 3n-, 4n-, 5n-evaporation channels are listed in Fig. 4, marked by the black, red, blue, magenta, olive lines, respectively. We found that the survival probability of more neutron number channels decreased rapidly, due to the fission decay being dominant in this nuclei region. The capture cross-sections of the reactions$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ($ \eta $ =0.68),$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ($ \eta $ =0.66),$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ ($ \eta $ =0.64) for producing new element Z=120 are listed in panel (d), marked by red dash lines, blue dash-dot lines and solid black lines, respectively. There is little difference between the three, due to the coupled effect of the strong Coulomb force and the deformation. Their compound nuclei are$ ^{305}{\rm{120}} $ ,$ ^{301}{\rm{120}} $ . The fusion probability is listed in Fig. 4. The two highly excited compound nuclei de-excited by evaporating light particles. The evaporation probability of 1n-, 2n-, 3n-, 4n-, and 5n-evaporation channels for the$ ^{305}{\rm{120}} $ ,$ ^{301}{\rm{120}} $ are shown in panel (f). It is found that the survival probability is relatively small, compared to the other two stages, which depress the synthesis cross sections strongly. Therefore, the predicted synthesis cross-sections of new SHE are highly dependent on the survival probability, where shell correction energy plays a crucial role.Figure 4. For the reactions of
$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ and and the reactions of$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ lead to new element with atomic number Z=119, 120 at wide incident energies, respectively. The capture cross-sections, fusion cross-section, and survival probability are listed in the three lists of panels. (color online)We multiplied the capture cross-section, the fusion probability, and the survival probability together to get the residual cross-sections of 2n-, 3n-, 4n-, 5n-, and 6n-evaporation channels which are marked by solid black lines, red dash lines, blue dash-dot lines, magenta dash-dot-dot lines, respectively, as shown in Fig. 5. The up-panels show the excitation functions of multiple neutron evaporation channels of the reactions
$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ $ \rightarrow ^{300}{\rm{119}} $ ,$ ^{50}{\rm{Ti}} $ +$^{247}{\rm{Bk}} \rightarrow$ $^{297}{\rm{119}}$ ,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ $ \rightarrow ^{297}{\rm{119}} $ . Panel (a) shows that the largest cross-section is 0.3 nb in the reaction$ ^{48}{\rm{Ca}} $ ($ ^{252}{\rm{Es}} $ , 3n)$ ^{297}{\rm{119}} $ at the excitation energy 34 MeV. Panel (b) shows that the largest cross-section is 0.4 nb in the reaction$ ^{50}{\rm{Ti}} $ ($ ^{247}{\rm{Bk}} $ , 3n)$ ^{294}{\rm{119}} $ at the excitation energy 38 MeV. Panel (c) shows that the largest cross-section is 0.001 nb in the reaction$ ^{54}{\rm{Cr}} $ ($ ^{243}{\rm{Am}} $ , 3n)$ ^{294}{\rm{119}} $ at the excitation energy 34 MeV. It is found that the reaction of$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ at excitation 38 MeV is the best to produce new element Z=119. The production cross-sections of the new superheavy element Z=119 are highly dependent on the entrance channels. The bottom panels show the excitation functions of multiple neutron evaporation channels of the reactions$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ $ \rightarrow ^{305}{\rm{120}} $ ,$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ $ \rightarrow ^{301}{\rm{120}} $ ,$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} \rightarrow $ $ ^{301}{\rm{120}} $ . Panel (d) displays the largest cross-section is 0.01 nb in the reaction$ ^{48}{\rm{Ca}} $ ($ ^{257}{\rm{Fm}} $ , 4n)$ ^{301}{\rm{120}} $ at the excitation energy 42 MeV, where the neutron number of the synthesized superheavy isotope$ ^{301}{\rm{120}} $ N=181 is so close to the superheavy island of stability. Panel (e) displays that the largest cross-section is 0.01 nb in the reaction$ ^{50}{\rm{Ti}} $ ($ ^{251}{\rm{Cf}} $ , 3n)$ ^{298}{\rm{120}} $ at the excitation energy 36 MeV. Panel (f) displays the largest cross-section is$ 5\times 10^{-3} $ nb in the reaction$ ^{54}{\rm{Cr}} $ ($ ^{247}{\rm{Cm}} $ , 4n)$ ^{297}{\rm{120}} $ at the excitation energy 46 MeV. Fig. 5 exhibits the influence of entrance channels on production cross-sections of new superheavy isotopes. The best collision combinations of synthesizing new superheavy elements are the reactions of projectile$ ^{50}{\rm{Ti}} $ induced reaction on the target$ ^{247}{\rm{Bk}} $ ,$ ^{251}{\rm{Cf}} $ .Figure 5. The evaporation residual cross sections of
$ ^{48}{\rm{Ca}} $ +$ ^{252}{\rm{Es}} $ $ \rightarrow $ $ ^{300}{\rm{119}} $ *,$ ^{50}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ $ \rightarrow $ $ ^{297}{\rm{119}}$ *,$ ^{54}{\rm{Cr}} $ +$ ^{243}{\rm{Am}} $ $ \rightarrow $ $ ^{297}{\rm{119}}$ * are listed in up-panels. The evaporation residual cross sections of$ ^{48}{\rm{Ca}} $ +$ ^{257}{\rm{Fm}} $ $ \rightarrow $ $ ^{305}{\rm{120}}$ *,$ ^{50}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ $ \rightarrow $ $ ^{301}{\rm{120}}$ *,$ ^{54}{\rm{Cr}} $ +$ ^{247}{\rm{Cm}} $ $ \rightarrow $ $ ^{301}{\rm{120}}$ * are listed in bottom-panels. (color online)From the investigation of the entrance channel effect on the production cross-section of specific superheavy nuclei, the best projectile-target combination of synthesizing the element Z = 119 is found to be
$ ^{46}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ . The ratio of N/Z for projectile isotopes might contribute to the formation cross-section or depress the synthesis probability for the specific SHN. To investigate the dependence of residual cross-sections of multiple neutrons evaporation channels on the isospin of the projectile, the selections of$ ^{44, 46, 48, 50, 52, 54}{\rm{Ti}} $ as the projectile bombarding on the target$ ^{247}{\rm{Bk}} $ have been made, which could lead to the new SHN with Z=119, as illustrated in Fig. 6, in which the black lines, red dash lines, blue dash-dot lines, magenta dash-dot-dot lines and short-dash lines indicate the excitation functions of the 2n-, 3n-, 4n-, 5n-, and 6n-evaporation channels, respectively. Panel (a) shows the excitation function of the reactions$ ^{44}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ , and the largest cross-section of the reactions$ ^{44}{\rm{Ti}} $ ($ ^{247}{\rm{Bk}} $ , 2n)$^{289}{\rm{119}}$ is 2.3 pb at an excitation energy of 36 MeV. Panel (b) shows the largest cross-section is 4.3 pb, corresponding to the reactions$ ^{46}{\rm{Ti}} $ ($ ^{247}{\rm{Bk}} $ , 2n)$ ^{291}{\rm{119}} $ at the excitation energy 30 MeV. Panel (c) shows the synthesis cross-sections of$ ^{293}{\rm{119}} $ ,$ ^{292}{\rm{119}} $ ,$ ^{291}{\rm{119}} $ are 1.5 pb, 0.6 pb, 0.1 pb in the reactions$ ^{48}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ respectively. Panel (d) presents the production cross sections of$ ^{295}{\rm{119}} $ ,$ ^{294}{\rm{119}} $ ,$ ^{293}{\rm{119}} $ are 0.3 pb, 0.4, and 0.1 pb, respectively. Panel (e) exhibits that the 3n- and 4n-evaporation channels are dominant in the reactions$ ^{52}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ , and have cross-sections of 0.02 pb, 0.04 pb, respectively. The 54Ti-induced reactions produce very low cross sections of SHN ($ \sigma < $ 0.01 pb). For producing new SHE with Z=119, the Ti-induced reactions present a high dependence of the production cross sections on the isospin of the projectile. It is worth mentioning that the 48Ca-induced reactions with$ ^{252}{\rm{Es}} $ and$ ^{257}{\rm{Fm}} $ have been predicted for the synthesis cross-section level, i.e. 0.1 pb for Z=119 and 0.01 pb for Z = 120, based on the DNS model. We found that the collisions of$ ^{44}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ and$ ^{46}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ , and$ ^{48}{\rm{Ti}} $ +$ ^{247}{\rm{Bk}} $ are suitable to synthesize new SHE with Z=119.Figure 6. The cross sections of 2n-, 3n-, 4n-, 5n-evaporation channels in the reactions of projectile
$ ^{44, 46, 48, 50, 52, 54}{\rm{Ti}} $ bombarding on target$ ^{247}{\rm{Bk}} $ are listed in these panels. (color online)To find the best combinations of the projectile Ti isotopes and target
$ ^{251}{\rm{Cf}} $ for synthesizing new SHE with Z=120, we have performed the calculations of the Ti-induced reactions systematically, as shown in Fig. 7, where the black lines, red dash lines, blue dash-dot lines, magenta dash-dot-dot lines and short-dash lines indicate the excitation functions of the 2n-, 3n-, 4n-, 5n-, and 6n-evaporation channels, respectively. The black dash lines mark the cross-section 0.1 pb in the up-panels. Figure 7 has a similar form to Fig. 6. Panel (a) is for the reactions$ ^{44}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ , which shows the largest cross section is around 0.2 pb for the 3n-channel. Panel (b) displays the$ ^{46}{\rm{Ti}} $ -induced reactions, where the 2n- and 3n-channels are dominant. The largest cross-section of the 2n-, and 3n-evaporation channels are about 1 pb, 0.6 pb in the reactions$ ^{46}{\rm{Ti}} $ ($ ^{251}{\rm{Cf}} $ , 2n)$ ^{295}{\rm{120}} $ and$ ^{46}{\rm{Ti}} $ ($ ^{251}{\rm{Cf}} $ , 3n)$ ^{294}{\rm{120}} $ , respectively. The projectile$ ^{48}{\rm{Ti}} $ -induced reactions could lead to the synthesis cross-section 0.02 pb for 3n-channel, as shown in panel (c). Panels (d), (e), (f) show the$ ^{50, 52, 54} {\rm{Ti-induced }}$ reactions that produced the extremely low cross sections ($ <0.01 $ pb). Fig. 7 has shown that production cross sections of new SHE with Z=120 are highly dependent on the isospin of the projectile. The most suitable combination of projectile-target is the reaction$ ^{46}{\rm{Ti}} $ +$ ^{251}{\rm{Cf}} $ which could synthesize SHN of$^{295}{\rm{120}}$ and$ ^{294}{\rm{120}} $ with the cross sections of 1 pb, 0.6 pb, respectively.
Production Cross-sections of New Superheavy Elements with Z = 119, 120 in Fusion-evaporation Reactions
doi: 10.11804/NuclPhysRev.39.2022112
- Received Date: 2022-10-29
- Rev Recd Date: 2022-11-26
- Available Online: 2023-04-26
- Publish Date: 2022-12-20
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Key words:
- new superheavy elements /
- production cross section /
- entrance effect /
- dinuclear system model
Abstract: We have calculated production cross sections of new superheavy elements with atomic number Z=119, 120 in the fusion-evaporation reactions of
Citation: | Zihan WANG, Penghui CHEN, Xianghua ZENG, Zhaoqing FENG. Production Cross-sections of New Superheavy Elements with Z = 119, 120 in Fusion-evaporation Reactions[J]. Nuclear Physics Review, 2022, 39(4): 421-433. doi: 10.11804/NuclPhysRev.39.2022112 |