Possibilities for synthesis of new neutron deficient isotopes of superheavy nuclei

Figures(10)

Get Citation
. doi: 10.1088/1674-1137/43/5/054105
.  doi: 10.1088/1674-1137/43/5/054105 shu
Milestone
Received: 2019-01-28
Article Metric

Article Views(25)
PDF Downloads(6)
Cited by(0)
Policy on re-use
To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

Possibilities for synthesis of new neutron deficient isotopes of superheavy nuclei

  • Department of Physics, Collaborative Innovation Center for Quantum Effects, and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081, China

Abstract: In order to search the optimal projectile-target combination to produce new neutron deficient isotopes of superheavy nuclei (SHN), the dependence of the evaporation residue cross section (ERCS) to synthesize SHN on the mass asymmetry and the isospin of colliding nuclei are analysed within the dinuclear system (DNS) concept. Predicted ERCSs for the production of new neutron deficient isotopes of SHN were found to be quite large with 36S projectile, and it is found that the production cross sections of SHN decrease slowly with the charged numbers of compound nuclei due to the increases in survival probability which $ W_{{\rm sur}} $ are not canceled by the decreasing $ P_{{\rm CN}} $.

    HTML

    1.   Introduction
    • The superheavy nuclei (SHN) production in the laboratory has drawn much attention because it is connected with whether there exists an island stability of SHN [1-5], and where it is located. Currently, there is a gap between the SHN synthesized by hot fusion and cold fusion reactions [6-11]. In order to fully understand the shell effects and other properties, and for developing the theoretical models which will be able to predict well the properties of SHN located beyond this area, the extension of the area of known isotopes of SHN is extremely important.

      In recent years, many efforts have been devoted to the investigation of the synthesis mechanism of SHN [12-25]. Many approaches are proposed to calculate the fusion probability [26-33]. However, no approach is currently predominant [34]. The dinuclear system (DNS) concept is one of them [16, 35-38]. Based on the DNS model calculated evaporation residue cross sections (ERCS) for the cold and hot fusion reactions leading to heavy and SHN are in good agreement with available experimental data [39-59].

      Selecting the optimal composition of the colliding nuclei is one of the most important aspects to successful synthesis of SHN. In order to fill the gap, several isotopes of actinide nuclei can be used as the targets. The beams of 36S, 40Ar and 44Ca as the projectils are also interesting. Recently, the first measurement of ERCSs in the complete fusion reaction 36S+238U and the observation of 270Hs have already been performed in experimental studies [60].

      One of the aims of present work is to study several fusion reactions leading to formation the same compound nucleus of unknown isotopes of SHN, and those between already obtained in cold and hot fusion. Usually, the fusion hindrance is smaller for the mass asymmetric reaction system, and hence the corresponding production cross section may be enhanced. Once the best projectile is selected, to search for the optimal condition of synthesis, it is necessary to study the dependence of the ERCS on the isospin composition of colliding nuclei. In the present work, the influence of target neutron number on capture cross section, fusion probability, and survival probability for the reactions 36S+236−244Pu are investigated in detail. In addition, we systematically study the ERCSs of the 36S bombarding targets of the actinide isotopic chain. The aims of our work is to predict the ERCSs of unknown neutron deficient isotopes of SHN.

    2.   Theoretical framework
    • The evaporation residue cross section (ERCS) in heavy-ion fusion reactions is calculated as the summation over all partial waves $ J $ [16],

      $ \begin{split} \sigma_{{\rm ER}}(E_{{\rm c.m.}}) = &\frac{\pi \hbar^{2}}{2\mu E_{{\rm c.m.}}}\sum_{J = 0}^{J_{{\rm max}}}(2J+1)T(E_{{\rm c.m.}}, J) \\ &\times P_{{\rm CN}}(E_{{\rm c.m.}}, J)W_{{\rm sur}}(E_{{\rm c.m.}}, J), \end{split} $

      (1)

      where $ E_{{\rm c.m.}} $ is the incident energy in the center-of-mass frame. $ T(E_{{\rm c.m.}}, J) $ is the transmission probability of the two colliding nuclei overcoming the Coulomb potential barrier in the entrance channel to form the DNS. The capture cross section $ \sigma_{{\rm cap}} = \displaystyle\frac{\pi \hbar^{2}}{2\mu E_{{\rm c.m.}}}\sum_{J}(2J+1)T(E_{{\rm c.m.}}, J) $ is calculated with an empirical coupled-channel approach [22, 61]. The $ P_{{\rm CN}} $ is the probability that the system evolves from a touching configuration to the compound nucleus in competition with the quasifission process. The last term $ W_{{\rm sur}} $ is the survival probability of the formed compound nucleus, which can be estimated with a statistic method [62].

    • 2.1.   Capture cross section

    • The capture cross section is:

      $ \sigma_{{\rm cap}}(E_{{\rm c.m.}}) = \frac{\pi\hbar^{2}}{2\mu E _{{\rm c.m.}}}\sum_{J}(2J+1)T(E_{{\rm c.m.}}, J), $

      (2)

      where the transmission probability can be written as

      $ \begin{split}& T(E_{{\rm c.m.}}, J) = \\&\int f(B) \frac{1}{1+\exp\left\{-\displaystyle\frac{2\pi}{\hbar\omega(J)}\left[E_{{\rm c.m.}}-B-\displaystyle\frac{\hbar^{2}}{2\mu R_{B}^{2}}J(J+1)\right]\right\}}{\rm d}B, \end{split} $

      (3)

      where $ \hbar\omega(J) $ is the width of the parabolic Coulomb barrier at the position $ R_{B}(J) $, and an empirical coupled channel method is used via a barrier distribution function which is taken as an asymmetric Gaussian form [54]. The nucleus-nucleus interaction potential with quadrupole deformation has been used, which is addressed in detail in Ref [51].

    • 2.2.   Fusion probability

    • The fusion dynamics are described as a diffusion process by numerically solving a set of two-variable master equation (ME) in the corresponding potential energy surfaces [22, 52]. The time evolution of the probability distribution function $ P(Z_{1}, N_{1}, \varepsilon_{1}, t) $ for fragment 1 with $ Z_{1} $ and $ N_{1} $ and with the local excitation energy $ \varepsilon_{1} $ at time $ t $ is described by the following ME:

      $ \begin{split} \frac{{\rm d}P(Z_{1}, N_{1}, \varepsilon_{1}, t)}{{\rm d}t} =& \sum_{Z'_{1}}W_{Z_{1}, N_{1};Z'_{1}, N_{1}}(t)\times[d_{Z_{1}, N_{1}}P(Z'_{1}, N_{1}, \varepsilon'_{1}, t)\\&-d_{Z'_{1}, N_{1}}P(Z_{1}, N_{1}, \varepsilon_{1}, t)]+\sum_{N'_{1}}W_{Z_{1}, N_{1};Z_{1}, N'_{1}}(t) \\& \times \![\!d_{Z_{1}, N_{1}}P(Z_{1}, N'_{1}, \varepsilon'_{1}, t)\!-\!d_{Z_{1}, N'_{1}}P(Z_{1}, N_{1}, \varepsilon_{1}, t)\!] \\&-[\Lambda_{{\rm qf}}(\Theta(t))+\Lambda_{fs}(\Theta(t))]P(Z_{1}, N_{1}, \varepsilon_{1}, t), \end{split} $

      (4)

      where $ W_{Z_{1}, N_{1};Z_{1}, N'_{1}} $ is the mean transition probability from channel ($ Z_{1}, N'_{1} $) to ($ Z_{1}, N_{1} $), while $ d_{Z_{1}, N_{1}} $ denotes microscopic dimensions corresponding to the macroscopic state ($ Z_{1}, N_{1} $) [17, 26, 63, 64], and will be shown later. The $ \varepsilon_{1} $ denotes the local excitation energy, and will be shown later. The sum is taken over all possible proton and neutron numbers that fragment $ Z'_{1} $, $ N'_{1} $ may take, but only one nucleon transfer is considered in the model.

      The probability $ P(Z_{1}, N_{1}, \varepsilon_{1}, t) $ distributed in the bottom of pocket will have the chance to decay out of the DNS, i.e. the evolution of the DNS along the variable $ R $ leads to the quasifission of the DNS, with corresponding quasifission rate $ \Lambda_{Z, N}^{{\rm qf}}(\Theta) $. In order to consider the influence of the DNS decay on the probability distribution $ P(Z_{1}, N_{1}, \varepsilon_{1}, t) $, we need to include the effect of quasifission rate in the ME. The quasifission rate $ \Lambda_{{\rm qf}} $ in Eq. (10) is estimated with one-dimensional Kramers formula [65, 66].

      $ \begin{split} \Lambda_{Z, N}^{{\rm qf}}(\Theta) =& \frac{\omega}{2\pi\omega^{B_{{\rm qf}}}}\left(\sqrt{\left(\frac{\Gamma}{2\hbar^{2}}\right)^{2}+(\omega^{B_{{\rm qf}}})^{2}}-\frac{\Gamma}{2\hbar}\right) \\ &\times\exp\left(-\frac{B_{{\rm qf}}(Z, N)}{\Theta(Z, N)}\right) .\end{split} $

      (5)

      The quasifission barrier $ B_{{\rm qf}} $ measures the depth of the pocket of the nucleus-nucleus interaction potential. The quasifission barrier $ B_{{\rm qf}} $ decreases with increasing $ Z $, for near symmetric configurations there is no minimum of the nucleus-nucleus potential [45, 47]. In the present work, if the nuclear-nucleus interaction potential has no minimum, we assumed that the height of the quasifission barrier $ B_{{\rm qf}} $ is 0.5 MeV. The temperature $ \Theta(Z, N) $ of the DNS is calculated with the expression $ \Theta(Z, N) = \sqrt{\varepsilon/a} $ with the local excitation energy $ \varepsilon $ of the DNS. The level density parameter is calculated with the expression $ a = A/12 $ ${\rm MeV}^{-1} $. Here, the $ \omega $ is the frequency of the harmonic oscillator approximating the potential along the internuclear distance around the bottom of the pocket. The frequency $ \omega^{B_{\rm{qf}}} $ is the frequency of the inverted harmonic oscillator approximating the interaction potential of two nuclei along the internuclear distance around the top of the quasifission barrier. The quantity $ \Gamma $ denotes the double average width of the contributing single-particle states. In the present work, constant values $ \Gamma = 2.8 $ MeV, $ \hbar\omega^{B_{\rm{qf}}} = 2.0 $ MeV and $ \hbar\omega = 3.0 $ MeV were used.

      Solving the Eq. (4) numerically, the time evolution of the probability distribution $ P(Z_{1}, N_{1}, \varepsilon_{1}, t) $ to find fragment 1 ($ Z_{1}+N_{1} $) with excitation energy $ \varepsilon_{1} $ at time $ t $ is obtained. All those components on the left side of the Businaro-Gallone (BG) point contribute to the compound nuclear formation. The fusion probability represents the Z-N configuration at the BG point beyond which the system falls into the fusion valley in the potential energy surface as a function of mass-charge asymmetry parameter. Therefore, the fusion probability $ P_{{\rm CN}} $ is the summation of $ P(Z_{1}, N_{1}, \varepsilon_{1}, t) $ from ($ Z_{1} = 1, N_{1} = 1 $) to ($ Z_{{\rm BG}}, N_{{\rm BG}} $) configurations. The compound nucleus formation probability at the minimum of the nucleus-nucleus potential ($ B_{m} $), which corresponding to a certain orientation of the colliding nuclei in the entrance channel, and for the angular momentum $ J $ is given by

      $ \begin{align} P_{{\rm CN}}(E_{{\rm c.m.}}, J, B_{m}) = \sum_{Z_{1} = 1}^{Z_{{\rm BG}}}\sum_{N_{1} = 1}^{N_{{\rm BG}}}P(Z_{1}, N_{1}, \varepsilon_{1}, \tau_{{\rm int}}, B_{m}). \end{align} $

      (6)

      The interaction time $ \tau_{{\rm int}} $ (this will be shown later) in the dissipative process of two colliding nuclei is dependent on the incident energy $ E_{{\rm c.m.}} $, $ J $ and $ B_{m} $, which is determined by using the deflection function method [67]. Finally, we obtain the fusion probability $ P_{{\rm CN}}(E_{{\rm c.m.}}, J) $ as

      $ \begin{align} P_{{\rm CN}}(E_{{\rm c.m.}}, J) = \int f(B_{m})P_{{\rm CN}}(E_{{\rm c.m.}}, J, B_{m}){\rm d}B_{m}, \end{align} $

      (7)

      where the barrier distribution function is taken in asymmetric Gaussian form [17].

      In order to numerically solve Eq. (4), we need to input interaction time and local excitation energy. The time interval between formation and break of the composite system is defined as the interaction time $ \tau_{{\rm int}} $. As shown in Fig 1 from the Ref. [67] that during this process the composite system rotates about its center of mass. On the one hand, for a given value $ J_{i} $ of the incident angular momentum, $ \tau_{{\rm int}}(J_{i}) $ is determined by the rotation of the composite system through the angle

      Figure 1.  The mean interaction times are shown as a function of the incident angular momentum \small$J$ for the 36S+250Cf, 40Ar+246Cm and 44Ca+242Pu reactions with the corresponding excitation energy $E_{{\rm CN}}^{*} = 40$ MeV.

      $ \Delta\vartheta(J_{i}) = \pi-\vartheta_{i}-\vartheta_{f}-\Theta(J_{i}), $

      (8)

      where the Coulomb angles $ \vartheta_{i} $ and $ \vartheta_{f} $ are given by the Coulomb trajectories in entrance and exit channels with the corresponding the energies $ E_{i} $, $ E_{f} $ and the angular momenta $ J_{i} $, $ J_{f} $ values, respectively.

      $ \vartheta_{i(f)} = \arcsin\frac{2b_{i(f)}/R+\varepsilon_{i(f)}}{\sqrt{4+\varepsilon_{i(f)}^{2}}}-\arcsin\frac{1}{\sqrt{(2/\varepsilon_{i(f)})^{2}+1}} , $

      (9)

      where $ \varepsilon_{i(f)} = \alpha/(E_{{\rm c.m.}}b_{i(f)}) $, $ \alpha = Z_{P}Z_{T}e^{2} $ and $b_{i(f)} =\hbar J_{i(f)}/ $$ \sqrt{2\mu E_{{\rm c.m.}}} $.

      The essential ingredient of the model is the determination of the deflection function $ \Theta(J_{i}) $ from the experimental angular distribution. However, this is achieved by introducing the parametrization [68]

      $ \Theta(J_{i}) = \Theta_{{\rm C}}(J_{i})-\beta\Theta_{{\rm gr}}^{{\rm C}}\frac{J_{i}}{J_{{\rm gr}}}\left(\frac{\delta}{\beta}\right)^{J_{i}/J_{{\rm gr}}}. $

      (10)

      The first term on the right hand side is the Coulomb deflection function. The second term describes the deviation from the Coulomb deflection function due to the nuclear interaction between projectile and target. The parameters $ \delta $ and $ \beta $ are determined by a fit of the differential cross section obtained from experimental data. The initial angular momentum is taken to be $ J_{i} = J $. The details of $ \delta $ and $ \beta $ are given in Ref. [69]. The grazing angular momentum $ J_{{\rm gr}} $ can be expressed:

      $ J_{{\rm gr}} = 0.22R_{{\rm int}}[A_{{\rm red}}(E_{{\rm c.m.}}-V(R_{{\rm int}}))]^{1/2}, $

      (11)

      the $ V(R_{{\rm int}}) $ denotes the interaction barrier at the interaction radius $ R_{{\rm int}} $. The $ A_{{\rm red}} $ is reduced mass.

      During this process the composite system rotates about its center of mass. The relation between $ \Delta\vartheta $ and $ \tau_{{\rm int}} $ is given by the integral

      $ \Delta\vartheta(J_{i}) = \int_{0}^{\tau_{int}}{\rm d}t\frac{{\rm d}\vartheta}{{\rm d}t} = \int_{0}^{\tau_{{\rm int}}}{\rm d}t\frac{\hbar J(t)}{\zeta_{{\rm rel}}(t)} $

      (12)

      with the time dependent angular momentum $ J(t) $ and relative moment of inertia $ \zeta_{{\rm rel}}(t) $. The dissipation of the relative angular momentum $ <J(t)> $ is described by

      $ <J(t)> = J_{{\rm st}}+(J_{i}-J_{{\rm st}})\exp(-t/\tau_{J}), $

      (13)

      where the limiting value $ J_{{\rm st}} $ given by the sticking condition $ J_{{\rm st}} = J_{i}\zeta_{{\rm rel}}^{0}/\zeta_{{\rm tot}}^{0} $. The relaxation time $ \tau_{J} $ is $ 1.5\times 10^{-21} $ s. For the relative and total moments of inertia we take the rigid-body values: $ \zeta_{{\rm rel}} = \mu R^{2} $ ($ \zeta_{{\rm rel}}^{0} = \mu R^{2}_{0} $) and $\zeta_{{\rm tot}} = \mu R^{2}+ $$ \displaystyle\frac{2}{5}m_{1}R_{1}^{2}+\displaystyle\frac{2}{5}m_{2}R_{2}^{2} $$ \left(\zeta_{{\rm tot}}^{0} = \mu R^{2}_{0}+\displaystyle\frac{2}{5}m_{1}R_{1}^{2}+\displaystyle\frac{2}{5}m_{2}R_{2}^{2} \right)$; where $ m_{1} $, $ m_{2} $, $ \mu $, $ R_{1} $, $ R_{2} $ are the masses, the reduced mass, and the radii of the fragments, respectively. The $ R_{0} $ is radius that two nuclei form a rotating composite system at close contact. The coupled Eqs. (8)-(13) are solved by iteration to obtained the interaction time $ \tau_{{\rm int}} $.

      For the next considered three 36S+250Cf, 40Ar+246Cm and 44Ca+242Pu reactions, the averaged interaction times are calculated by deflection function method [67-69]. In Fig. 1, we plot the mean interaction time as a function of the incident angular momentum $ J $ with the corresponding excitation energies $ E_{{\rm CN}}^{*} = 40 $ MeV. One can see from in Fig. 1 that the interaction time of the composite system is long for partial waves with small incident angular momentum $ J $. In addition, we found that interaction time decreases with increasing $ J $. From Fig. 1 we also observed the decreasing of interaction time with decreasing mass asymmetry in the entrance channel with the special excitation energy and angular momentum $ J $. This is because the Coulomb repulsion increases gradually with the decrease of mass asymmetry.

      The local excitation energy is defined as [17, 70]

      $ \begin{split} \varepsilon =& E_{x}-[U(Z_{1}, N_{1}, Z_{2}, N_{2}, \beta_{1}, \beta_{2}, J) \\&-U(Z_{P}, N_{P}, Z_{T}, N_{T}, \beta_{P}, \beta_{T}, J)], \end{split} $

      (14)

      where the dissipation energy $ E_{x} $ of the composite system is converted from the relative kinetic energy loss. The dissipation energy $ E_{x} $ is related to the minimum of the nucleus-nucleus potential ($ B_{m} $) and is determined for each initial relative angular momentum $ J $ by the parametrization method of the classical deflection function.

      $ \begin{align} E_{x} = E_{{\rm c.m.}}-B_{m}-\frac{<J(t)>(<J(t)>+1)\hbar^{2}}{2\zeta_{{\rm rel}}}-<E_{{\rm rad}}(J, t)> \end{align}, $

      (15)

      $ \begin{align} <E_{{\rm rad}}(J, t)> = E_{{\rm rad}}^{i}\exp\left[-\frac{\tau^{J}_{{\rm int}}}{\tau_{{\rm rad}}}\right] .\end{align} $

      (16)

      The $ \tau_{{\rm rad}} $ denotes the relaxation time the dissipation of the radial kinetic energy. The quantity $ E_{{\rm rad}}^{i} $ denotes the initial radial kinetic energy at the interaction radius. The radial energy at the initial state $ E_{{\rm rad}}^{i}(J, 0) =E_{{\rm c.m.}}-B_{m}-EJ_{i} (J_{i} + $ $1)\hbar^{2}/ (2\zeta_{{\rm rel}}) $. The initial angular momentum is taken to be $ J_{i} = J $. The value of $ \tau_{{\rm rad}} $ is $ 3\times10^{-22} $ s [68]. As can be seen from Fig. 1, the angular momentum is within the range of our research, and the interaction time $ \tau^{J}_{{\rm int}} $ is much larger than $ \tau_{{\rm rad}} $. Therefore, for the current three reaction systems, the $ <E_{{\rm rad}}(J, t)> $ value at $ E_{{\rm CN}}^{*} = 40 $ MeV is infinitely close to zero.

      The second term of Eq. (14) is the driving potential energy [16, 17] of the system for the nucleon transfer of the DNS, which is:

      $ \begin{split} U(Z_{1}, N_{1}, \beta_{1}, \beta_{2}, J) =& B(Z_{1}, N_{1}, \beta_{1})+B(Z_{2}, N_{2}, \beta_{2})-B(Z, N, \beta) \\& +U_{C}(Z_{1}, Z_{2}, \beta_{1}, \beta_{2})\\&+U_{N}(Z_{1}, N_{1}, Z_{2}, N_{2}, \beta_{1}, \beta_{2}, J) \\ =& Q_{gg}+U_{C}(Z_{1}, Z_{2}, \beta_{1}, \beta_{2})\\&+U_{N}(Z_{1}, N_{1}, Z_{2}, N_{2}, \beta_{1}, \beta_{2}, J) ,\end{split} $

      (17)

      where $ Z = Z_{1}+Z_{2} $ and $ N = N_{1}+N_{2} $, the $ \beta_{i} (i = 1, 2) $ and $ \beta $ represent quadrupole deformations of the two fragments and the compound nucleus, respectively. The $ B(Z_{1}, N_{1}, \beta_{1}) $, $ B(Z_{2}, N_{2}, \beta_{2}) $ and $ B(Z, N, \beta) $ are the binding energies of two deformed nuclei and the compound nucleus [71], respectively. The $ Q_{gg} $ ($Q_{gg} = B(Z_{1}, N_{1}, \beta_{1})+B(Z_{2}, N_{2}, \beta_{2})- B(Z, N, \beta) $) denote the ground state $ Q $ value. In the present work, the deformation parameters and binding energies are taken from Refs. [72, 73]. Wong's formula [74] is adopted to calculate the Coulomb interaction, and the nuclear potential is calculated with Skyrme-type interaction without considering the momentum and spin dependence [75]. Here the inner fusion barrier appears on the driving potential energy surface during evolution on mass (charge) asymmetry axis. The inner fusion barrier is determined by the difference between the maximum value of the driving potential and its value at the point corresponding to the initial charge asymmetry of the considered reaction. In order to form a compound nucleus, a inner fusion barrier must be overcome.

      In Eq. (4), $ W_{Z_{1}, N_{1};Z_{1}, N'_{1}} $, $ d_{Z_{1}, N_{1}} $, $ \Lambda_{{\rm qf}} $, and $ \Lambda_{{\rm fs}} $ are all depended on the local excitation energy of the DNS. The transition probability is related to the local excitation energy, for neutron transition probability $ W_{Z_{1}, \;N_{1},\; \beta_{1},\; \beta_{2};\;Z_{1},\;N'_{1},\; \beta_{1},\; \beta_{2}} $ which can be written as [63, 64]

      $ \begin{split} W_{Z_{1}, N_{1}; Z_{1}, N'_{1}}(t) =& \frac{\tau_{{\rm mem}}(Z_{1}, N_{1}, \varepsilon_{1};Z_{1}, N'_{1}, \varepsilon'_{1})} {\hbar^{2}d_{Z_{1}, N_{1}}d_{Z_{1}, N'_{1}}} \\ & \times\sum_{ii'}|<Z_{1}, N'_{1}, \varepsilon'_{1}, i'|V(t)|Z_{1}, N_{1}, \varepsilon_{1}, i>|^{2}, \end{split} $

      (18)

      where $ i $ denotes all remaining quantum numbers. The memory time $ \tau_{{\rm mem}} $

      $ \begin{split} \tau_{{\rm mem}}(Z_{1}, N_{1}, \varepsilon_{1};Z_{1}, N'_{1}, \varepsilon'_{1}) = \hbar\sqrt{2\pi}\{<V^{2}(t)>_{Z_{1}, N_{1}, \varepsilon_{1}} \\ +<V^{2}(t)>_{Z_{1}, N'_{1}, \varepsilon'_{1}}\}^{-1/2}, \end{split} $

      (19)

      can be interpreted as the coherence time for the transitions between the subsets ($ Z_{1}, N_{1}, \varepsilon_{1} $) and ($ Z_{1}, N'_{1}, \varepsilon'_{1} $) [63, 64]. Where $ <V^{2}(t)>_{Z_{1}, N_{1}, \varepsilon_{1}} $ and $ <V^{2}(t)>_{Z_{1}, N'_{1}, \varepsilon'_{1}} $ stand for the average expectation value with $ Z_{1}, N_{1}, \varepsilon_{1} $ and $ Z_{1}, N'_{1}, \varepsilon'_{1} $ fixed, respectively. One can see that the memory time $ \tau_{{\rm mem}} $ depends on neutron number $ N_{1} $, proton number $ Z_{1} $ and local excitation energy $ \varepsilon_{1} $. For 36S+250Cf reaction, the memory time $ \tau_{{\rm mem}}(Z = 16, N = 20;Z = 16, N = 21) $ is $ 0.75\times10^{-22} $ s when the excitation energy $ E_{{\rm CN}}^{*} $ = 40 MeV.

      The transition probability of Eq.(18) can be written as

      $ \begin{split} W_{Z_{1}, N_{1};Z_{1}, N'_{1}}(t) =& \frac{\tau_{{\rm mem}}(Z_{1}, N_{1}, \varepsilon_{1};Z_{1}, N'_{1}, \varepsilon'_{1})} {\hbar^{2}d_{Z_{1}, N_{1}}d_{Z_{1}, N'_{1}}} \\& \times\{[\omega_{11}(Z_{1}, N_{1}, \varepsilon_{1}; \varepsilon'_{1}) \\& +\omega_{22}(Z_{1}, N_{1}, \varepsilon_{1}; \varepsilon'_{1})]\delta_{N'_{1}, N_{1}} \\ &+\omega_{12}(Z_{1}, N_{1}, \varepsilon_{1}; \varepsilon'_{1})\delta_{N'_{1}, N_{1}-1} \\& +\omega_{12}(Z_{1}, N_{1}, \varepsilon_{1}; \varepsilon'_{1})\delta_{N'_{1}, N_{1}+1}\}, \end{split} $

      (20)

      where

      $ \begin{split} \omega_{kk'}(Z_{1}, N_{1}, \varepsilon_{1}; \varepsilon'_{1}) =& \sum_{k, k'N'_{1}}|<Z_{1}, N'_{1}, \varepsilon'_{1}, i'|V_{k, k'}|Z_{1}, N_{1}, \varepsilon_{1}, i>|^{2} \\ =& d_{Z_{1}, N_{1}}<V_{k, k'}V^{+}_{k, k'}>. \end{split} $

      (21)

      The averages in Eqs. (18), (19) and (21) are carried out by using the method of spectral distributions [76, 77]. We obtain

      $ \begin{split} <V_{k, k'}V^{+}_{k, k'}> =& \frac{1}{4}U^{2}_{kk'}g_{k}g_{k'}\Delta_{kk'}\Delta\varepsilon_{k}\Delta\varepsilon_{k'} \\ &\times\left[\Delta_{kk'}^{2}+\frac{1}{6}\left(\Delta\varepsilon^{2}_{k}+\Delta\varepsilon^{2}_{k'}\right)\right]. \end{split} $

      (22)

      which contains some fixed independent parameters $ U_{kk'}(t) $ and $ \Delta_{kk'}(t) $. In present work, the strength parameters $ U_{kk'}(t) $ are taken as [63]

      $ U_{kk'}(t) = \frac{g_{1}^{1/3}\cdot g_{2}^{1/3}}{g_{1}^{1/3}+g_{2}^{1/3}}\cdot \frac{1}{g_{k}^{1/3}\cdot g_{k'}^{1/3}}\cdot 2\gamma_{kk'}. $

      (23)

      In our calculation $ \Delta_{11}(t) $ = $ \Delta_{12}(t) $ = $ \Delta_{22}(t) $ = $ \Delta_{21}(t) $ = 2, and the dimensionless strength parameters $ \gamma_{11} $ = $ \gamma_{12} $ = $ \gamma_{22} $ = $ \gamma_{21} $ = 3 are taken. Due to the excitation, a valence space $ \Delta\varepsilon_{k} $ is formed symmetrically around the Fermi surface. Only the particles in the states within this valence space are actively involved in the excitation and transfer [63, 64].

      $ \begin{align} \Delta\varepsilon_{k} = \sqrt{\frac{4\varepsilon_{k}}{g_{k}}}, \varepsilon_{k} = \varepsilon\frac{A_{k}}{A}, g_{k} = \frac{A_{k}}{12} (k = 1, 2). \end{align} $

      (24)

      Here $ \varepsilon $ deontes the local excitation energy of the DNS. The microscopic dimension is [63, 64]

      $ \begin{align} d_{Z_{1}, N_{1}}(m_{1}, m_{2}) = \left(\begin{array}{c} N_{1} \\ m_{1} \end{array}\right) \left(\begin{array}{c} N_{2} \\ m_{2} \end{array}\right). \end{align} $

      (25)

      There are $ N_{k} = g_{k}\Delta\varepsilon_{k} $ valence states and $ m_{k} = N_{k}/2 $ valence nucleons in $ \Delta\varepsilon_{k} $.

    • 2.3.   Survival probability

    • The survival probability of the compound nucleus at excitation energies mainly via emission of light particles and $ \gamma $-decay to survive against fission. In present work as well as in many other Refs. [23-25], the $ \gamma $-decay width and the other charged particles are always neglected at high excitation energies of interest in hot fusion reactions compared with evaporation of successive emission neutrons for simplicity. The survival probability of the excited compound nucleus in the deexcitation process by means of the neutron evaporation in competition with fission is expressed as the following:

      $ \begin{align} W_{{\rm sur}}(E^{*}_{{\rm CN}}, x, J) = F(E^{*}_{{\rm CN}}, x, J)\prod_{i = 1}^{x}\left[\frac{\Gamma_{n}(E^{*}_{i}, J)}{\Gamma_{n}(E^{*}_{i}, J)+\Gamma_{f}(E^{*}_{i}, J)}\right]_{i}, \end{align} $

      (26)

      where, $ F(E^{*}_{{\rm CN}}, x, J) $ is the realization probability of the $ xn $ channel at the excitation energy $ E^{*}_{{\rm CN}} (E_{{\rm c.m.}}+Q) $ of the compound nucleus with the angular momentum $ J $, $ i $ the index of evaporation step, $ \Gamma_{n} $ and $ \Gamma_{f} $ are the partial widths of neutron emission and fission.

      The partial width for emission of a neutron from a compound nucleus with the excitation energy $ E_0 $ is given by Weisskopf formula

      $ \Gamma_{n} = \frac{gm_{n}\sigma_{{\rm inv}}}{\pi^2\hbar^2\rho_{0}(E_0-\delta_0)}\int_{0}^{E_0-B_n-\delta_n}\rho_{n}(E_0-B_n-\delta_n-\varepsilon)\varepsilon {\rm d}\varepsilon , $

      (27)

      where $ m_{n} $ and $ g $ are the mass and spin degeneracy of the emitted neutron, $ \sigma_{{\rm inv}} $ is the cross section for the formation of the decaying nucleus in the inverse process, $ \rho_{0}(E_{0}-\delta_0) $ is the level density of the parent nucleus at the thermal excitation energy corrected for its pairing energy $ \delta_0 $ and $ \rho_{n}(E_0-B_n-\delta_n-\varepsilon) $ is the corresponding level density of daughter nucleus after emitting a neutron. $ B_n $ and $ \delta_n $ are the neutron separation energy and the pairing energy of the daughter nucleus, respectively.

      The fission width can be expressed in terms of the transition state theory as

      $ \Gamma_{f}^{{\rm BW}} = \frac{1}{2\pi\rho_{0}(E_0-\delta_0)}\int_{0}^{E_0-B_f-\delta_f}\rho_{n}(E_0-B_f-\delta_f-\varepsilon) {\rm d}\varepsilon , $

      (28)

      where $ \rho_{n}(E_0-B_f-\delta_f-\varepsilon) $ is the level density of the fissile nucleus at the saddle configuration. The calculations of the width of the fission channel are performed taking into account the effects of nuclear viscosity and the fission delay time,

      $ \Gamma_{f} = \frac{\hbar\omega_{{\rm gs}}}{T\omega_{{\rm sd}}}\left[\sqrt{1+\left(\frac{\beta}{2\omega_{{\rm sd}}}\right)^2}-\frac{\beta}{2\omega_{{\rm sd}}}\right]\times\Gamma_{f}^{{\rm BW}}, $

      (29)

      where the curvatures of the potential at the ground-state ($ \omega_{{\rm gs}} $) and saddle point ($ \omega_{{\rm sd}} $), and the reduced friction parameter $ \beta $ have been fixed with the default values $ \hbar\omega_{{\rm gs}} = 2.0 $ MeV, $ \hbar\omega_{{\rm sd}} = 2.4 $ MeV and $ \hbar\beta = 3.0 $ MeV, respectively.

      The back-shift Fermi-gas model at energies of hot-fusion reaction of interest is used to determine the level density,

      $ \rho(U, J) = \frac{(2J+1)\exp{\left[2\sqrt{aU}-\displaystyle\frac{J(J+1)}{2\sigma^2}\right]}}{24\sqrt{2}\sigma^3 a^{1/4} U^{5/4}}, $

      (30)

      with $ \sigma^2 = \displaystyle\frac{\Theta_{{\rm rigid}}}{\hbar^2}\sqrt{\frac{U}{a}} $, $ \Theta_{{\rm rigid}} = \displaystyle\frac{2}{5}m_{u}AR^2 $, $ U = E-\delta $. The back shifts $ \delta = -\Delta $ (odd-odd), 0 (odd A) and $ \Delta $ (even-even), respectively, are related to the neutron and proton paring gap $ \Delta = 1/2[\Delta_n(Z, N)+\Delta_p(Z, N)] $ which is employed from mass differences of neighboring nuclei [78]. The dependence of the level density parameter $ a $ on the shell correction and the excitation energy was initially proposed

      $ a(U, Z, N) = \tilde{a}(A)\left[1+E_{{\rm sh}}\frac{f(U)}{U}\right] $

      (31)

      with $ \tilde{a}(A) = \alpha A+\beta A^{2/3} $ and $ f(U) = 1-\exp{(-\gamma_{\rm D} U)} $. It is worth noting that the differences between the corresponding level density parameters are mainly related to different shell corrections and thus one should use these parameters at the same shell correction energies. In present work parameters $ \alpha = 0.1337 $, $ \beta = -0.06571 $ and $ \gamma_{\rm D} = 0.04884 $ [78] determined by fitting to experimental level density data at the help of the microscopic shell correction from FRDM95 [79] are adopted to calculate the level density using in the evaporation calculations.

      We calculated the angular momentum dependence of the transmission, fusion and survival probabilities as shown in Fig. 2 for the reaction 36S+250Cf at incident energies 169.64 MeV. The values of the three stages decrease obviously with increasing the relative angular momentum. So in the following estimation of the ERCSs, we cut off the maximal angular momentum at $ J_{{\rm max}} $ = 30. Similar result is also illustrated in Ref. [80].

      Figure 2.  Calculated transmission, fusion and survival probabilities as functions of the relative angular momenta in the reaction 36S+250Cf at excitation energies of the compound nucleus of 40 MeV.

    3.   Numerical results and discussions
    • Very recently, in order to review our calculated abilities on the ERCSs to synthesize superheavy nuclei using DNS model, the hot fusion reactions producing SHN with $ Z\geqslant 104 $ are systematically studied [81]. The results of systematic calculation show that the current theoretical method can describe the ERCS of SHN. In the present work, the calculations for all reactions were performed with the same parameters and assumptions.

    • 3.1.   Predictions of probable projectile-target combinations

    • In order to predict the most suitable projectile-target combination from the probable ones, production cross sections of new neutron deficient SHN with charged numbers $ Z $ = 108−114 are analyzed systematically with 36S, 40Ar, and 44Ca projectiles. In the present work, based on the framework of the DNS model, we calculated the ERCSs of the SHN based on the actinide targets 249−252Cf, 245−248Cm, and 241−244Pu with the projectiles 36S, 40Ar, and 44Ca as shown in Fig. 3. The ERCSs decreases by about one order of magnitude with increasing charge number of projectile from $ Z = 16 $ to $ Z = 20 $. This is due to the strong decreasing of fusion probability $ P_{{\rm CN}} $ and the increasing of the quasifission with increasing asymmetry in the entrance channel.

      Figure 3.  (color online) Evaporation residue excitation functions in the production of isotopes of the superheavy nuclei Fl in the reactions 36S+249−252Cf, 40Ar+245−248Cm, and 44Ca+241−244Pu.

      In Fig. 3(c) the calculated ERCSs are shown for the production of new neutron deficient isotopes of Fl in the fusion reactions of 36S with 251Cf targets and for the 40Ar+247Cm fusion reaction leading to the same compound nucleus as in the 44Ca+243Pu reaction. The parameters relevant to the exit channels, such as the neutron separation energies and the fission barrier heights, are nearly identical for both reactions at the same excitation energy (neglecting small differences in angular momentum of the compound nucleus after its formation). However, as can be seen from Fig. 3(c), the use of an 40Ar beam is less favorable than 36S. This is attributable to a worse fusion probability of the 40Ar+247Cm fusion reaction because the dinuclear system gets more symmetric and fusion probability decreases. Our calculations also demonstrated that the use of a 44Ca beam instead of 36S decreases the yield of the same SHN owing to a worse fusion probability. Calculations were performed for the reactions 36S+243−246Cm, 40Ar+239−242Pu, and 44Ca+235−238U to produce the superheavy nuclei Cn as shown in Fig. 4. The strong dependence of the calculated ERCSs for the production of SHN on the mass asymmetry in the entrance channel makes the 36S projectile most promising for the further synthesis of SHN.

      Figure 4.  (color online) Evaporation residue excitation functions in the production of isotopes of the superheavy nuclei Cn in the reactions 36S+243−246Cm, 40Ar+239−242Pu, and 44Ca+235−238U.

    • 3.2.   Influence of the target neutron number on ERCSs

    • The calculated maximal ERCSs 3$ n $, 4$ n $ and the corresponding optimal excitation energies of the compound nuclei in the 3$ n $ and 4$ n $ evaporation channel are presented in Fig. 5 for the reactions 36S+APu as functions of the mass number A of the target, respectively. For the 3n and 4n emission channel for 36S+APu reaction, it is seen from in Fig. 5(b) that the maximum ERCSs increases with the increase of neutron number to the maximum value and then decreases with the increase of neutron number. From the lower part of Fig. 5(c), it can be seen that the excitation energies of 3 and 4 neutron emission decreases slowly with the increase of neutron number. In order to analyze the trend of the change above, the whole process of SHN synthesis needs to be investigated in detail. Now we investigate how influence of target neutron number on capture cross section, fusion probability, and survival probability.

      Figure 5.  The isospin dependence from the 36S+APu hot fusion reactions: (a) the Q values for the fusion reactions 36S+APu; (b)the maximal evaporation residue cross sections as functions of the target mass number A, for the 3n and 4n emission channels; (c) the corresponding excitation energies of the compound nuclei.

      As can be seen from the Fig. 6(a), the capture cross section as a function of the incident energy are quite close for these three reactions due to a slight difference of Coulomb barriers. Fig. 6(b) shows the capture cross section $ \sigma_{{\rm cap}} $ as a function of the excitation energy of the compound nucleus. In the lower excitation energy region $ E^{*}_{{\rm CN}}<37 $ MeV, and the capture cross sections for the reactions 36S+236Pu is larger than those of the reaction systems 36S+244Pu because of the large negative $ Q $ values ($ E_{{\rm CN}}^{*} = E_{{\rm c.m.}}+Q $) of the former reactions. When increasing excitation energy increase beyond 37 MeV, the differences caused by the Q values become less important, the capture cross sections almost tend to be all consistent.

      Figure 6.  (a) The calculated capture cross sections as functions of incident energy in the center-of-mass frame for the reactions 36S+236, 240, 244Pu. (b) The calculated capture cross section are functions of excitation energy of the compound nucleus.

      Consider only the effects of mass asymmetry on the fusion probability, when the neutron number in the target nucleus increases, the dinuclear system gets more asymmetric and fusion probability increases [29, 82]. In Fig. 7(a) shows that our calculated fusion probability are functions of excitation energy of the compound nucleus for the reactions 36S+236, 240, 244Pu. However, we are aware during the calculation for the 36S+236Pu and 36S+240Pu, the fusion probability $ P_{{\rm CN}} $ decreases with increasing neutron number in the lower excitation energy region $ E^{*}_{{\rm CN}}<45 $ MeV. When increasing excitation energy increase beyond 45 MeV, the differences of fusion probability among three reactions become very small, the results tend to be all consistent. One found that the irregular behavior of the fusion probability $ P_{{\rm CN}} $ changes with increasing neutron number of the targets. The fusion probability depends on the details of the driving potential, which is decided by the ground state $ Q_{gg} $ value of the nuclei in each DNS and their interactions [53]. Therefore, our results show that in addition to the mass asymmetry, the reaction $ Q_{gg} $ value plays an important role in the fusion probability.

      Figure 7.  (a) The calculated fusion probability are functions of excitation energy of the compound nucleus for the reactions 36S+236, 240, 244Pu. (b) The calculated survival probabilities as functions of the compound nucleus excitation energy.

      The survival probability of the hot compound nucleus sensitively depends on the value of neutron separation energy $ B_{n} $ and fission barrier $ B_{f} $. The fission barriers of 3$ n $ evaporation channel for compound nuclei 272−280Ds basically increase with the increase of neutron number to the maximum value, and then decrease with the increase of neutron number [79]. The survival probabilities of 3$ n $ evaporation channel are shown in Fig. 7(b) for the compound nuclei 272, 276, 280Ds. One can see that the survival probabilities increase with the increase of neutron number for excitation energies lower than 50 MeV. Therefore, for 3$ n $ evaporation channel, the increase of survival probability of compound nuclei from 272Ds to 275Ds is not canceled by an decreasing capture cross section and fusion probability. The calculated maximal ERCSs $ \sigma_{3n} $ is larger in the 36S+239Pu reaction than in the 36S+236−238Pu reactions due to the larger value of survival probability. For 4$ n $ evaporation channel, the change of target neutron number has little influence on fusion probability and capture cross section. The variation trend of 4$ n $ ERCS with the neutron number of target nuclei is mainly determined by the survival probability. Therefore, 4$ n $ evaporation channel corresponding to the ERCS basically increase with the increase of neutron number to the maximum value and then decrease with the increase of neutron number.

    • 3.3.   Production cross sections of neutron-deficient SHN

    • Figure 8 shows the comparison of the calculated ERCS with the experimental data in the reaction 36S+238U. The measured ERCSs of the 3$ n $ and 4$ n $ channels are denoted by solid squares and open circles [60], respectively. One find that for the 3$ n $ channel the calculated results is closer to the experimental data. We also realized that one calculated ERCS of the 4$ n $ channel in the reaction 36S+238U peaks at excitation energy approximate 44 MeV, which is smaller than the excitation energy used in the experiment for 238U(36S, 4$ n $)270Hs [60]. However, for 4$ n $ evaporation channel, the peak position is not clear due to lack of experimental data. Taking into account the experimental error bars one can say that the agreement between our calculated ERCS and the experimental value [60] are good for the 36S+238U reaction.

      Figure 8.  (color online) The excitation functions for the 36S+238U reaction. The calculated results and experimental data [60] are denoted by lines and symbols, respectively. The measured ERCSs of the 3n and 4n channels are denoted by solid squares and open cycles, respectively. The calculated 3n, 4n, and 5n channels are indicated by the solid, dashed and dotted lines, respectively.

      Our studies the isospin dependence of the ERCS of some SHN based on the same assumptions with one set of parameters. The maximal ERCS, $ \sigma_{{\rm ER}} $(pb), for 3$ n $ and 4$ n $ emission channels out of 36S bombarding actinide isotopic chains: AU, ANp, AAm, ACm, ABk and ACf are shown in Fig. 9 as a function of the mass number of the target. From Fig. 9 one can see that the isotopes of target nucleus with the largest neutron excess are favorable for the most cases of hot fusion with 36S projectile. Except in the 3$ n $ emission channel for 36S+ACm reaction, in all other channels it is seen that the ERCSs basically increase with increasing neutron numbers, though sometimes not very distinct.

      Figure 9.  The isospin dependence of the maximal evaporation residue cross sections from the hot fusion reactions: (a) 36S+AU, (b) 36S+ANp, (c) 36S+AAm, (d) 36S+ACm, (e) 36S+ABk and (f) 36S+ACf as functions of the target mass number A, for the 3n and 4n emission channels.

      Now we investigate how influence of target neutron number on ERCS. Similar to the results of the reactions 36S+APu, our calculations show that the capture cross sections for the neutron deficient target nucleus is larger than neutron rich one in the lower excitation energy region for the above projectile target combinations. We are also aware that during the calculation the fusion probability $ P_{{\rm CN}} $ for 36S+AU, 36S+ANp, 36S+AAm, 36S+ACm, 36S+ABk and 36S+ACf the $ P_{{\rm CN}} $ change with increasing neutron number of the target is not regular. The behavior of the fusion probability $ P_{{\rm CN}} $ changes with increasing neutron number of the targets is not regular, which depends on the details of the driving potential, which is decided by the properties of nuclei in each DNS, and their interactions.

      For 3$ n $ emission, in most cases, the increases in $ W_{{\rm sur}} $ are not canceled by the decreasing $ \sigma_{{\rm cap}} $ and irregular changing $ P_{{\rm CN}} $ with increasing neutron number. Therefore, the 3$ n $ evaporation channel corresponding to the ERCS basically increase with the increase of neutron number. However, for compound nuclei 278−286Cn, 3$ n $ evaporation channel 275−283Cn corresponding to the fission barriers [79] basically decrease with the increase of neutron number to the minimum value and then increase with the increase of neutron number. Therefore, the ERCSs of the reactions 36S+ACm decrease with the increase of neutron number to the minimum value and then increase with the increase of neutron number.

      For 4$ n $ evaporation channel, the change of target neutron number has little influence on fusion probability and capture cross section. The variation trend of 4$ n $ ERCS with the neutron number of target nuclei is mainly determined by the survival probability. Therefore, 4$ n $ evaporation channel corresponding to the ERCS basically increase with the increase of neutron number. One can see that from Fig. 9 that it is found that the ERCSs of SHN decrease slowly with the charged numbers of compound nuclei from $ Z = 108 $ to $ Z = 114 $ due to the increases in survival probability $ W_{{\rm sur}} $ which are not canceled by the decreasing $ P_{{\rm CN}} $.

      Currently, there is a gap between the SHN synthesized by cold fusion and those by hot fusion [83]. One can found that quite large cross sections ($ \sigma_{1n}\geqslant $ 1 pb) for many reaction channels used to fill the gap. For example, as shown in Figs. 9(b) given the predicted excitation function of $ xn $ ERCSs for the reaction 36S+ANp. For the 36S+235Np reaction, the maximal ERCSs of the 4$ n $ channel is 2.74 pb at $ E_{{\rm c.m.}} = 168.39 $ MeV ($ E_{{\rm c.m.}} = E_{{\rm CN}}^{*}+Q $). It is 17.14 pb at $ E_{{\rm c.m.}} = 165.11 $ MeV for the 36S+237Np reaction. Through the analysis of Fig. 5(c) and Fig. 9, we found that the nucleus 267, 269Mt, 268, 272, 274−276Ds, 273, 275, 276Rg, 274−276, 278−280Cn, 279−281Nh and 281−283Fl may be produced. One can see from in Fig. 10, at fixed charge asymmetry in the entrance channel, the optimal excitation energy $ E_{{\rm CN}}^{*} $ of compound nucleus decrease with increasing neutron excess in the target. One can expect large ERCSs in the actinide-based reactions with the 36S beam. And based on the targets 235−237Np, 241−243Am, and 247−249Bk the production of odd SHN with $ Z = $109, 111, and 113, are shown promising.

      Figure 10.  The isospin dependence of the excitation energies of the compound nuclei corresponding maximal evaporation residue cross sections from the hot fusion reactions: (a) 36S+AU, (b) 36S+ANp, (c) 36S+AAm, (d) 36S+ACm, (e) 36S+ABk and (f) 36S+ACf as functions of the target mass number A, for the 3n and 4n emission channels.

    4.   Conclusions
    • In order to study the conditions for synthesizing some new neutron deficient SHN, the projectiles 36S, 40Ar and 44Ca bombarding some actinide isotope chains are systematically studied within the DNS model. Our results show that the strong dependence of the calculated ERCSs for the production of SHN on the mass asymmetry in the entrance channel makes the 36S projectile most promising for the further synthesis of new neutron deficient SHN. The influence of the target neutron number on ERCSs in hot fusion reactions is also investigated. There are certain probability to produce new neutron deficient such as using 36S to bombard 232−238U, 236−244Pu, 242−250Cm and 249−251Cf. Then one can expect to produce new neutron deficient SHN of the Hs, Ds, Cn and Fl with the ERCS larger than from about 1 pb, up to 10 pb. Some new nuclides of Mt, Rg, and Nh may be produced by the reaction channels 36S+235−237Np, 241−243Am, 247−249Bk with the ERCS larger than 1 pb. Hopefully, the results will shed light to experimentally synthesize some new nuclide.

Reference (83)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return