Higher Multipole Deformations Research Articles

Possibility to form Z=120 via the Ni64+U238 reaction using the dynamical cluster-decay model

According to different theoretical studies, the next magicity for the proton number should occur at $Z=114$, 120, or 126 and for the neutron number $N=184$. Superheavy nuclei of interest for the forthcoming synthesis of the isotopes with $Z=119$, 120 are investigated. Many reactions have yet to be studied in order to find the possible incoming channels for the formation of $Z=120$. In this work, synthesis of superheavy element 120 in terms of the fission and quasifission cross sections via $^{64}\mathrm{Ni}+^{238}\mathrm{U}$ reaction is evaluated and discussed. We have explored the possibility of formation of $Z=120$ via $^{64}\mathrm{Ni}+^{238}\mathrm{U}$ reaction, using the experimental data from Kozulin , Phys. Lett. B 686, 227 (2010). Some experimental efforts have been made to synthesize $^{302}120$, via Ni-induced and Cr-induced reaction, i.e., $^{64}\mathrm{Ni}+^{238}\mathrm{U}$ reaction at five ${E}^{*}$'s (excitation energies) and the $^{54}\mathrm{Cr}+^{248}\mathrm{Cm}$ reaction at only one energy, respectively. In this work, we have studied the Ni-induced reaction at given energies by including higher multipole deformations ${\ensuremath{\beta}}_{\ensuremath{\lambda}i}$ $(\ensuremath{\lambda}=2,3,4$; $i=1,2)$, and compact orientations ${\ensuremath{\theta}}_{ci}$ using the coplanar degree of freedom $(\mathrm{\ensuremath{\Phi}}={0}^{\ensuremath{\circ}})$ within the framework of the dynamical cluster-decay model (DCM). The neck-length parameter is the only one, which is fixed in reference to the observed data for fission cross section $({\ensuremath{\sigma}}_{\mathrm{ff}})$ calculated for mass region $A/2\ifmmode\pm\else\textpm\fi{}20$, and quasifission cross section $({\ensuremath{\sigma}}_{\mathrm{qf}})$ for the incoming channel of $^{64}\mathrm{Ni}+^{238}\mathrm{U}$ reaction. Our calculations for Ni-induced reaction have shown a good concurrence with the experimental data for quasifission and fission cross sections along with the DCM-calculated estimated and predicted cross sections for evaporation residues (ERs), which can be used for future references. Our results demonstrate the insignificant compound nucleus formation possibility ${P}_{\text{CN}}$ $(\ensuremath{\ll}1)$ for $Z=120$ from Ni-induced reaction because of the very low order of evaporation residues; thus, this work is not supporting this incoming channel for the formation of $Z=120$.

Impact of noncoplanar degrees of freedom on quasifission contributions with the estimation of unobserved decay channels for the study of Pt*196 using the dynamical cluster-decay model

In Phys. Rev. C 98, 041603 (2018) it was demonstrated that the noncoplanar degrees of freedom (or azimuthal angle ${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{0}$), including higher-multipole deformations ${\ensuremath{\beta}}_{\ensuremath{\lambda}i}$ ($\ensuremath{\lambda}=2,3,4;\phantom{\rule{4pt}{0ex}}i=1,2$), and the compact orientations ${\ensuremath{\theta}}_{ci}$ are the most essential set of parameters in the dynamical cluster-decay model (DCM), in order to study heavy-ion reactions. In this work, we study the comparison between the coplanar ($\mathrm{\ensuremath{\Phi}}={0}^{\ensuremath{\circ}}$) and noncoplanar (${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{\ensuremath{\circ}}$) configurations, including higher multipole deformations, for $^{196}\mathrm{Pt}^{*}$ formed via the $^{132}\mathrm{Sn}+^{64}\mathrm{Ni}$ reaction. This reaction was earlier studied [M. K. Sharma et al., J. Phys. G: Nucl. Part. Phys. 38, 055104 (2011)] by one of our collaborators but only with $\mathrm{\ensuremath{\Phi}}={0}^{\ensuremath{\circ}}$, including quadrupole deformations, ${\ensuremath{\beta}}_{2i}$ alone having ``optimum'' orientations (${\ensuremath{\theta}}_{\mathrm{opt}.}$), with the result of noncompound nucleus [nCN, equivalently quasi-fission (qf)] contribution at higher energies. The only parameter of the DCM is the neck length $\mathrm{\ensuremath{\Delta}}R$, whose value for the nuclear proximity potential used here remains within its range of validity ($\ensuremath{\approx}2$ fm). The evaporation residues (ERs) and fission cross section (${\ensuremath{\sigma}}_{ff}$) are calculated in reference to available experimental data at near- and sub-barrier energies for $^{196}\mathrm{Pt}^{*}$. As a result of inclusion of ${\mathrm{\ensuremath{\Phi}}}_{c}\ensuremath{\ne}{0}^{\ensuremath{\circ}}$, the nCN contribution approaches zero at higher energies and corresponds to ${P}_{\mathrm{CN}}=1$, which is rather significant for the $\mathrm{\ensuremath{\Phi}}={0}^{\ensuremath{\circ}}$ configuration. Secondly, in this attempt we have tried to explore the evolution of the neck-length parameter ($\mathrm{\ensuremath{\Delta}}R$), which will help us to estimate the cross sections of unobserved decay channels.

Systematic decay analysis of 202Po∗ compound nucleus using Dynamical Cluster-decay Model

The decay analysis of [Formula: see text]Po[Formula: see text] compound nucleus (CN), formed via [Formula: see text]Ca+[Formula: see text]Gd reaction, with inclusion of additional degrees-of-freedom, i.e., the higher multipole deformations, the octupole ([Formula: see text]) and hexadecupole ([Formula: see text]), the corresponding “compact” orientations ([Formula: see text]), and noncoplanarity degree-of-freedom ([Formula: see text]0), is investigated within the collective clusterization approach. The Quantum Mechanical Fragmentation Theory (QMFT)-based Dynamical Cluster-decay Model (DCM), wherein the point of penetration [Formula: see text], fixed via the in-built neck-length parameter [Formula: see text] in [Formula: see text] (equivalently, the “barrier lowering” [Formula: see text]), is used to best fit the channel cross-section ([Formula: see text]) and predict the quasi-fission (qf)-like nCN cross-section [Formula: see text], if any, and the fusion–fission ([Formula: see text]) cross-sections. We also look for other target-projectile (t-p) combinations for the synthesis of CN [Formula: see text]Po[Formula: see text].

Study on the compound nucleus fusion probability PCN in 12C +93Nb reaction at above barrier energies using different degrees-of-freedom

In this work, we extend our earlier study [S. Chopra, Hemdeep, A. Kaur and R. K. Gupta, Phys. Rev. C 93 (2016) 024603] of [Formula: see text] reaction at below- and near- to above-barrier energies for both coplanar ([Formula: see text]) and noncoplanar ([Formula: see text]) degrees-of-freedom. Our main aim is to see the texture of variation of compound nucleus (CN) fusion probability [Formula: see text] at all the experimentally available center-of-mass energies ([Formula: see text]) in the range 41–69[Formula: see text]MeV, using the dynamical cluster-decay model (DCM). In this study, we worked for both degrees-of-freedom, having compact configurations ([Formula: see text]) and including higher multipole deformations (quadrupole to hexadecapole, [Formula: see text]) of nuclei. In the work of above-mentioned reference, for [Formula: see text]Ag[Formula: see text] (weakly fissioning nuclear system), we found a discrepancy in [Formula: see text], i.e., increasing function with increasing [Formula: see text], belongs to superheavy nuclei for the case of [Formula: see text] [see Fig. Fig.4 of [A. Kaur, S. Chopra and R. K. Gupta, Phys. Rev. C 90 (2014) 024619], but this erroneous result moved to correct one after the inclusion of [Formula: see text] (decreasing with increasing [Formula: see text], weakly fissioning class), which encouraged us to check the trend of [Formula: see text] at all available energies. Our evaluation framework shows the noncoplanar configuration, with higher multipole deformations [Formula: see text] included, as the most probable configuration for studying the heavy-ion reactions [S. Chopra, Hemdeep, P. Kaushal and R. K. Gupta, Phys. Rev. C 98 (2018) 041603(R)]. Second, our interest is to check the consistency of experimental data, where the experimentalists have given the data with the mixing of three different experiments for same reaction. In this study, we have found that our results are in good agreement and consistent with only the latest experimental data at five [Formula: see text]’s (=41.097, 47.828, 54.205, 60.051 and 65.454[Formula: see text]MeV), i.e., showing large ([Formula: see text]90%) noncompound nucleus contribution (or equivalently quasi-fission/Incomplete fusion) in the (total) fusion cross-section.

Signatures of higher-multipole deformations and non-coplanarity as essential, additional degrees-of-freedom in heavy-ion reactions

Eloquent display of signatures of including higher-multipole (octupole and hexadecupole) deformations βλi, i=1,2,λ=2–4, and non-coplanar degrees-of-freedom Φ are shown here for the first time as essential, additional variables in low-energy heavy-ion reactions (HIR), within the dynamical cluster-decay model (DCM) of the collective clusterization process. In other words, a description in terms of quadrupole-deformed, “optimally” oriented coplanar nuclei is not sufficient, which therefore calls for both higher-multipole deformations (β3i and β4i; i=1,2) and non-coplanarity (Φ≠0∘) as the additional degrees-of-freedom. Such a convincing, real result appears in terms of the non-compound-nucleus (nCN) effect, the nCN cross section σnCN-content in σfusion, which is different for different compound nuclei (CN), i.e., CN specific, varying from an almost complete impure to pure CN decay while going successively from (β2i, θ2iopt, Φ=0∘) to (β2i-β4i, “compact” oriented θci, Φ≠0∘), which is further independent of the radioactive or nonradioactive nature of CN formed in different entrance channels, i.e., also independent of entrance channel target-projectile nuclei. This study plus our earlier study of spontaneous C14-cluster radioactivity provide a new set of variables, in terms of higher-multipole deformations and non-coplanarity degrees-of-freedom, to explore the real outcome of any low-energy HIR (plus spontaneous decay), which could in fact be already close to Nature.

Distinguishing Features of Radioactive Compound Nucleus Decays within the Dynamical Cluster Decay Model

In this paper, we are interested to study the distinguishing features of the decaying radioactive compound nuclei 246Bk* and 220Th*, using the Dynamical Cluster-decay Model (DCM) with deformation β and non-coplanar degree-of-freedom Φ. 246Bk* and 220Th* have so-far been studied within the DCM, using quadrupole deformations (β2i), “optimum” orientations (θopt) of the two nuclei lying in the same plane (Φ=0o), which shows that there is a non-compound nucleus (nCN) content in the observed data. The first turning point Ra (equivalently, the neck-length ∆R in Ra=R1+R2+∆R), which fixes both the preformation and penetration paths, is used to best fit the measured evaporation residue (ER) and fusion-fission (ff) cross sections, σER, σff, respectively, in 220Th* and 246Bk*, formed via different entrance channels. In this work, we subsequently add higher multipole deformations, the octupole and hexadecupole (β3i, β4i), `compact’ orientations θci and Φ≠00, and look for their effects on the nCN contribution predicted by the DCM calculations referenced above.

Evaporation residue cross-section in the decay of 254No* formed in 206Pb + 48Ca and its isotopic dependence using other Pb targets within the dynamical cluster-decay model

The dynamical cluster-decay model (DCM), with deformation and orientation effects included, is used to calculate the fusion evaporation residue cross-sections σxn for x=1,2,3 and 4 neutrons emission in a fusion reaction 206Pb + 48Ca → 254No* at various 48Ca-beam energies Elab=212.7–242.5 MeV (equivalently, E⁎=19.8–43.9 MeV). Considering the higher multipole deformations up to hexadecapole deformation β4i and the sticking moment-of-inertia IS, the DCM with pocket formula for nuclear proximity potential is shown to give a good description of the measured individual light-particle (here neutrons) decay channels for configurations of “hot, compact” orientations θci, within one parameter fitting of the neck-length ΔR. A check on some of the variables involved in DCM shows that (i) spherical configurations give nearly the same result as above for deformed and oriented ones; (ii) the non-sticking moment-of-inertia INS gives unphysical results; and (iii) configurations of “cold, elongated” orientations do not fit the data at all. Furthermore, for the four different isotopes of 204,206,207,208Pb-based reactions, the dependence of, say, the 2n-emission yield σ2n on the isotopic composition of the compound nucleus is also studied within the DCM for “hot” fusion process. Of all the four Pb-isotopes and three excitation energies E⁎ considered, at each E⁎, the ΔR is largest for compound system 256No*, followed by 255No*, 254No* and smallest for 252No*, which means to suggest that the neutrons emission occur earliest for 256No*, then for 255No*, 254No* and finally by 252No*, in complete agreement with experimental data according to which compound system 256No* has the highest cross-section and 252No* the lowest with 255No* and 254No* lying in between. This result is related to the double magicity of both the target (208Pb) and projectile (48Ca) nuclei, as well as to the experimentally known result of projectile with a larger number of neutrons (here the target nucleus Pb) showing an increase in the production cross-section of superheavy nuclei, and is shown to be mainly due to the penetrability factor P in the compound nucleus decay cross-section.

Neutron-halo structure of light nuclei studied with effects of deformations and orientations included

Based on the cluster-core model, the effects of nuclear deformations and orientations on the halo structure of the observed and proposed cases of neutron-halo nuclei is analyzed. The calculations are performed for the deformed structures using quadrupole (β2) deformations with ‘optimum’ orientations as well as including higher multipole deformations (β2-β4) with the ‘compact’ (hot) orientations. The interesting result is that, although potential energy surfaces are modified with the inclusion of deformation effects up to β2, but the 1n- and 2n-halo nature remains intact for almost all cases investigated here, except for 17B and 22C nuclei. However, in some cases (22O, 26F, 27F), the choice of higher multipole deformations up to hexadecapole is shown to be rather sensitive. In addition, the relevance of the use of different nuclear proximity potentials is also explored in the context of the halo nature of neutron-rich light nuclei. The possible role of Q-value and angular momentum effects are also addressed.

Effects of deformations and orientations in the fission of the actinide nuclear system254Fm*formed in the11B + 243Am reaction

We have studied the decay of actinide nuclear system ${}^{254}$Fm${}^{*}$ formed in ${}^{11}$B $+$ ${}^{243}$Am reaction using the dynamical cluster decay model (DCM), with choices of spherical, quadrupole deformation ${\ensuremath{\beta}}_{2}$ alone and higher multipole deformations ${\ensuremath{\beta}}_{2}$--${\ensuremath{\beta}}_{4}$. For ${\ensuremath{\beta}}_{2}$ deformations, the optimum orientations ${\ensuremath{\theta}}_{i}^{\mathrm{opt}}$ are used whereas for higher multipole deformations the compact orientations ${\ensuremath{\theta}}_{i}^{c}$ of decaying fragments are taken in to account. Besides static-${\ensuremath{\beta}}_{2}$ deformations, the effects of dynamical-${\ensuremath{\beta}}_{2}$ deformations are also explored. The calculated cross sections find excellent agreement with the available experimental data with spherical as well as deformed choices of fragmentations, enabling us to account for the role of important nuclear deformation effects in the ${}^{11}$B-induced nuclear reaction. Spontaneous decay of ${}^{254}$Fm with cold elongated configuration and optimum orientation is also worked out. The mass distributions of excited fermium isotopes in the neighborhood of ${}^{254}$Fm${}^{*}$ are also explored. In addition, the roles of temperature, angular momentum, and fission fragment anisotropies are investigated in the context of the chosen reaction.

Role of higher-multipole deformations in exoticC14cluster radioactivity

We have studied nine cases of spontaneous emission of $^{14}\mathrm{C}$ clusters in the ground-state decays of the same number of parent nuclei from the trans-lead region, specifically from $^{221}\mathrm{Fr}$ to $^{226}\mathrm{Th}$, using the preformed cluster model (PCM) of Gupta and collaborators, with choices of spherical, quadrupole deformation (${\ensuremath{\beta}}_{2}$) alone, and higher-multipole deformations (${\ensuremath{\beta}}_{2}$, ${\ensuremath{\beta}}_{3}$, ${\ensuremath{\beta}}_{4}$) with cold ``compact'' orientations ${\ensuremath{\theta}}^{c}$ of decay products. The calculated $^{14}\mathrm{C}$ cluster decay half-life times are found to be in nice agreement with experimental data only for the case of higher-multipole deformations (${\ensuremath{\beta}}_{2}$-${\ensuremath{\beta}}_{4}$) and ${\ensuremath{\theta}}^{c}$ orientations of cold elongated configurations. In other words, compared to our earlier study of clusters heavier than $^{14}\mathrm{C}$, where the inclusion of ${\ensuremath{\beta}}_{2}$ alone, with ``optimum'' orientations, was found to be enough to give the best comparison with data, here for $^{14}\mathrm{C}$ cluster decay the inclusion of higher-multipole deformations (up to hexadecapole), together with ${\ensuremath{\theta}}^{c}$ orientations, is found to be essential on the basis of the PCM. Interestingly, whereas both the penetration probability and assault frequency work simply as scaling factors, the preformation probability is strongly influenced by the order of multipole deformations and orientations of nuclei. The possible role of $Q$ value and angular-momentum effects are also considered in reference to $^{14}\mathrm{C}$ cluster radioactivity.

Establishing the island of stability for superheavy nuclei via the dynamical cluster-decay model applied to a hot fusion reaction 48Ca + 238U → 286112*

Considering different magic shells such as Z = 126, 120 or 114, N = 184 or Z = 120, N = 172 for the superheavy mass region, the dynamical cluster-decay model (DCM), with deformation and orientation degrees of freedom of colliding nuclei or decay fragments included, is used to study the complete excitation functions of a ‘non-equatorial’ compact hot-fusion reaction 48Ca + 238U → 286112* (orientation angle θc = 72° for 238U; θc = 90° for ‘equatorial’ compact). For the higher multipole deformations taken up to hexadecapole deformations β4i and configurations with ‘compact’ orientations θci, the DCM gives a good description of the individual light-particle decay channels σxn (x = 3 and 4 neutrons), and other decay channels, the fusion–fission σff and quasi-fission σqf cross-sections, at various incident energies or compound nucleus excitation energies E*, within a single parameter description, the neck-length parameter ΔR. Within the Strutinsly renormalization procedure, in each case, the shell corrections are obtained from an ‘empirical’ formula with the corresponding liquid-drop energies adjusted to give the experimental binding energies. This is done for all the mass (and charge) fragmentations of the compound system. Of all the four choices of magic numbers considered, the evaporation residue cross-sections (σER = σ3n + σ4n, the sum of light-particle, neutron-channel cross-sections) remain the largest and nearly the same for Z = 126, N = 184 or Z = 120, N = 184, but the fusion–fission cross-sections σff are always the highest for Z = 120, N = 184. Noting that the quasi-fission process is not affected by the magicity of shells, this study supports Z = 120 and N = 184 as the strongest magic numbers for the center of an island of stability for superheavy elements.

Cluster radioactivity with effects of deformations and orientations of nuclei included

Based on the preformed cluster model (PCM) of Gupta and collaborators, we have extended our recent study on ground-state cluster decays to parent nuclei resulting in daughters other than spherical {sup 208}Pb, i.e., to deformed daughters, and the very new cases of {sup 14}C and {sup 15}N decays of {sup 223}Ac, and {sup 34}Si decay of {sup 238}U, taking nuclei as spherical, quadrupole deformed ({beta}{sub 2}) alone, and with higher multipole deformations up to hexadecapole ({beta}{sub 2}, {beta}{sub 3}, {beta}{sub 4}) together with the 'optimum' orientations of cold decay process. Except for {sup 14}C decays of {sup 221}Fr, {sup 221-224,226}Ra, and {sup 225}Ac where higher multipole deformations up to {beta}{sub 4} are found essential, the quadrupole deformation {beta}{sub 2} alone is found good enough to fit the experimental data. Because the PCM treats the cluster-decay process as the tunneling of a preformed cluster, the deformations and orientations of nuclei modify both the preformation probability P{sub 0} and tunneling probability P, and hence the decay half-life, considerably.

Effect of octupole and higher deformations on Coulomb barrier

The effect of octupole deformation, β 3 , and the higher multipole deformations, β 6 and β 8 , on the distribution of barriers in orientation degrees of freedom, is studied. Coulomb barriers are derived in the frame work of the double folding model with the realistic M3Y nucleon–nucleon interaction and its density dependent version. 48Ca + 244Pu spherical-deformed nuclear interacting pair is considered, as an example, to study the effect of deformation parameters on the height and position of the Coulomb barrier. Although the dependence of the Coulomb barrier parameters on the higher deformations is complicated, numerically, if it is treated in microscopic way, we found a simple linear variation of barrier parameters with the different orders of deformation. We found that the variation of the barrier parameters with deformation exactly follows the change of the half density radius of the deformed nucleus in the direction of the separation vector between the centers of mass of the interacting nuclei. This suggests a simple and straightforward way to predict the behavior of the barrier parameters with different orders of deformations. We compared the results of present work with a similar recent study of the same quantities based on simple expression derived by Wong for the Coulomb part and proximity approach for the nuclear part of heavy ion potential, respectively.

ROLE OF STATIC DEFORMATION AND COMPACT ORIENTATION OF TARGET NUCLEUS IN MEASURED FUSION, FUSION-FISSION AND CAPTURE CROSS-SECTIONS OF 244Pu+48Ca REACTION

The dynamical cluster-decay model (DCM), with deformations and orientation degrees of freedom of the incoming nuclei and of outging fragments included, is used to study the excitation functions of the "equatorial" compact hot fusion reaction 244 Pu +48 Ca →292114* (compact orientation angle θc=90° for 244 Pu ). Considering the higher multipole deformations up to hexadecapole deformation β4 and configurations with "compact" orientation θc, the model is shown to give a good description of the measured individual light-particle decay channels σxn, here x=3, 4 and 5, and other decay channels, the fusion-fission σff and quasi-fission σqf (equivalently, capture σ cap ) with in one parameter fitting, the neck length ΔR. The quasi-fission is also considered as a cold process with an elongated "polar" configuration. The xn-channel cross-sections for collisions between nuclei with static deformations at their respective compact orientations are shown to be much more than for the case of the nuclei taken to be spherical, signifying the increase in fusion threshold for an intermediate hot fusion reaction to be associated with the static deformation of the target nucleus and its orientation at the point of collision in its path toward the (spherical) compound nucleus. The shell effects in both the potential and kinetic energy (the mass parameters) terms of the Hamiltonian are shown to be important. The free parameter ΔR of the model is shown to depend strongly on limiting angular momentum, which in turn depends on the use of sticking or non-sticking moment of inertia for angular momentum effects. For the sticking moment of inertia, the evaporation residue (neutron emission) is shown to occur almost promptly (largest ΔR), followed by the competing (hot/cold) quasi-fission and ending finally with fusion-fission of hot compound nucleus. Different ΔR's (equivalently, relative separations) for the three processes means to predict that the processes ER, ff and qf happen in different time-scales, in agreement with the indications of experiments.

Higher-multipole deformations and compactness of hot fusion reactions

The effect of adding the higher-multipole deformations ${\ensuremath{\beta}}_{6}$ and ${\ensuremath{\beta}}_{8}$, and the octupole deformation ${\ensuremath{\beta}}_{3}$ (in addition to quadrupole and hexadecapole deformations ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$), on the distribution of barriers in orientation degrees of freedom is studied for a ``compact'' configuration of spherical-plus-deformed or deformed-plus-deformed nuclei in hot fusion reactions. Though ${\ensuremath{\beta}}_{3}$ is known to be nonzero for only a few nuclei, its role toward compactness of hot fusion reactions is found to be as important as that of ${\ensuremath{\beta}}_{4}$. With ${\ensuremath{\beta}}_{3}$ included, depending on its sign and magnitude, the belly-to-belly compact, bbc (or equatorial compact, ec), configuration due to ${\ensuremath{\beta}}_{4}$ changes to not-belly-to-belly compact, nbbc (or not-equatorial compact, nec), and vice versa. Similarly, ${\ensuremath{\beta}}_{6}$ is found to be as important as ${\ensuremath{\beta}}_{3}$ and/or ${\ensuremath{\beta}}_{4}$ for spherical-plus-deformed nuclei, but is rather insignificant for collisions involving deformed-plus-deformed nuclei. On the other hand, the addition of ${\ensuremath{\beta}}_{8}$ is shown to be insignificant also for spherical-plus-deformed nuclei.

Compactness of theCa48induced hot fusion reactions and the magnitudes of quadrupole and hexadecapole deformations

Based on fragmentation theory extended to include the orientation degrees of freedom and higher multipole deformations up to hexadecapole deformations, the compactness of $^{48}\mathrm{Ca}$ induced reactions on various actinides is studied for Ds ($Z=110$) to 118 nuclei. It is shown that the reactions leading to $Z\ensuremath{\ge}114$ nuclei are ``compact'' hot fusion reactions at $\ensuremath{\theta}={90}^{\ifmmode^\circ\else\textdegree\fi{}}$ orientation angles (equatorial compact or ec; collisions that are in the direction of the minor axis of the deformed reaction partner), but the ones for $Z<114$ nuclei are compact at $\ensuremath{\theta}<{90}^{\ifmmode^\circ\else\textdegree\fi{}}$ (not-equatorial compact or nec). The phenomenon of ``barrier distribution in orientation degrees of freedom'' is observed for the first time to be related to the magnitudes of both the quadrupole and hexadecapole deformations of the deformed reaction partner. The ec configurations are obtained for the cases of quadrupole deformation alone and with small (including negative values) hexadecapole deformations. The presence of large (positive) hexadecapole deformations result in the nec configurations. These results are found to be quite general, applicable also to other lighter targets such as W and Ra with the $^{48}\mathrm{Ca}$ beam and to Pb based reactions. Furthermore, for compact hot fusion reactions, in addition to the $^{48}\mathrm{Ca}$ reaction valley, a number of other new reaction valleys (target-projectile combinations) are obtained, the most important one (next to $^{48}\mathrm{Ca}$) being the $^{54}\mathrm{Ti}$ nucleus used previously in Pb based cold fusion reaction studies but now proposed with deformed actinide nuclei such as $^{226}\mathrm{Ra}$, $^{232}\mathrm{Th}$, $^{238}\mathrm{U}$, and $^{242}\mathrm{Pu}$.

Optimum orientations of deformed nuclei for cold synthesis of superheavy elements and the role of higher multipole deformations

For collisions between deformed and oriented nuclei, the fragmentation theory is extended for the generalized nuclear proximity potential, with deformations included up to the hexadecupole deformations. For co-planar nuclei, the orientations are shown to get optimized (uniquely fixed) by the signs of their quadrupole deformations alone, not affected by the signs of their hexadecupole deformations. The optimum orientations are obtained for both the ‘hot compact’, and ‘cold elongated’ configurations of any two colliding nuclei. The hexadecupole deformations are shown to help fusion (hot or cold), depending on the choice of the reaction partners. Calculations are made for the 208Pb- and 48Ca-induced reactions and the neighbouring deformed nuclei. The calculated fragmentation potentials for optimally oriented nuclei, compared with both nuclei taken spherical, show that the excitation energy of the potential energy minima is significantly lowered for cold (elongated) fusion of deformed nuclei, but it remains nearly the same for at least the asymmetric hot (compact) fusion reactions. A number of new minima (target–projectile combinations) arise due to the cold and nearly symmetric hot fusion of deformed, optimally oriented nuclei.

Collective modes oftri-nuclear molecules

A geometrical model for tri-nuclear molecules is presented. Ananalytical solution is obtained provided the nuclei, which are taken to beprolately deformed, are connected in line to each other. Furthermore, thetri-nuclear molecule is composed of two heavy and one light cluster, thelattersandwiched between the two heavy clusters.A basis is constructed in which Hamiltonians of more generalconfigurationscan be diagonalized.In the calculation of the interaction between theclusters higher multipole deformations are taken into account, includingthehexadecupole one. A repulsive nuclear core is introduced in the potentialin orderto ensure a quasi-stable configuration of the system. The model is appliedto threenuclear molecules, namely 96Sr + 10Be + 146Ba,108Mo + 10Be + 134Te and112Ru + 10Be + 130Sn.