Preamble

Dynamics of light nuclei produced in the massive transfer reactions Zi-Han Wang , Ya-Ling Zhang and Zhao-Qing Feng 1 School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China (Dated: July 14, 2025) Within the framework of the dinuclear system (DNS) model by implementing the cluster transfer into the dissipation process, we systematically investigated the energy spectra and the angular distri- bution of the preequilibrium clusters (n, p, d, t, Be) in the massive transfer reactions Pt near the Coulomb barrier energies. It is found that the neutron emission is the most probable in com- parison with the charged particles and the yields are comparable with the hydrogen isotopes in magnitude. The preequilibrium clusters are mainly produced from the projectile-like and target-like fragments in the evolution of dinuclear system. The kinetic energy spectra manifest the Boltzmann distribution and the Coulomb potential influences the structure. The preequilibrium clusters follows the angular distribution of multinucleon transfer fragments.

PACS number(s):

Keywords

Preequilibrium cluster emission; Massive transfer reaction; Dinuclear system model I. INTRODUCTION The cluster structure in a atomic nucleus is a spatially located subsystem consisting of strongly related nucleons with much greater internal binding energy than external ones, which can be treated as a whole without considering its internal structure [ ]. In 1968, Ikeda proposed that the nuclear cluster states tend to occur in excited states near the cluster threshold energy [ In some weakly bound nuclei, the cluster structure is more obvious, and the cluster structure is also ubiquitous in light nuclei, for example, the configuration of Li being composed of a particle and a deuteron, the 2 structure for Be, 3 ]. The most convenient way to study the cluster structure inside a nucleus is to sep- arate the cluster via the pick-up or stripping reactions.

The theoretical explanation of the preequilibrium reac- tion was initially developed through the exciton model.

Semi-classical theories was less successful in explaining the angular distribution of emitted particles. The Boltz- mann master equation theory was mainly used to calcu- late the energy spectra of particles emitted in nucleon- induced reactions and heavy ion reactions. Details can be found in the review paper [ ]. On the other hand, the emission of preequilibrium clusters in transfer reactions around the Coulomb barrier is also an important physi- cal problem. The emission of preequilibrium clusters is a complex process, which is related not only to the cluster structure of the collision system, but also to the dynam- ics of the reaction. In the treatment of nuclear structure, the cluster state is the overlap of the single particle wave functions.

In the nuclear reaction, the formation of a preequilibrium particle is different from the cluster emit- ted during the de-excitation of a composite nucleus, and the pre-equilibrium cluster is formed before the forma- tion of compound nucleus. Its emission continues until the formation of the composite nucleus, and the pree- quilibrium cluster may be emitted from any fragments during the reaction.

Cluster emission provides impor- tant information for the study of single-particle states or multiparticle correlation of a nuclei, and it is a powerful tool for nuclear spectroscopy [ Moreover, the clus- ter emission in intermediate and high energy heavy-ion collisions is also important for investigating the nuclear fragmentation and the little-bang nucleosynthesis [ Since the multinucleon transfer (MNT) reactions and deep inelastic heavy ion collisions were proposed in the 1970s [ ], a large number of experiments have been carried out to measure the double differential cross sections, the angular distributions and the energy dis- tributions of different reaction systems. However, it is worth noting that there has been relatively little research on pre-equilibrium cluster emission in transfer reaction- s, both experimentally and theoretically. In the 1980s, scientists at RIKEN in Japan and at IMP in China have measured the preequilibrium cluster emission of the transfer reactions of ] and ], respectively. The an- gular distributions, kinetic energy spectra and total pro- duction cross sections of the emitted particles were mea- sured in experiments. As we all know, since the concept of superheavy stable island was proposed in the 1960s, the synthesis of superheavy nuclei has become an im- portant frontier in the field of nuclear physics. In the past few decades, 15 kinds of the superheavy elements = 104 118 [ ] have been synthesized artificially by hot fusion or cold fusion reaction. However, due to the limitations of the projectile-target materials and ex- perimental conditions, the fusion evaporation reaction is difficult to reach the next period of the periodic table.

With the MNT reactions, we can generate many nuclei depending on the transfer channels, and with the devel-

opment of the separation and detection technology, MNT reaction may be the most promising method to synthe- size unknown superheavy elements. This mechanism has been applied to the production of heavy and superheavy isotopes [ The study of the pre-equilibrium cluster emission in the MNT reaction is not only of great significance for understanding the cluster structure of the collision sys- tem, but also for exploring the formation mechanism of the cluster, the kinetic information of the reaction pro- cess and the nuclear astrophysical process.

The High Intensity Accelerator Facility (HIAF) built in Huizhou, China, has a large-energy range and a wide species of particle beams [ ], which provides a good experimental platform for the study of nuclear cluster structures and cluster emission.

In this work, we have systematically investigated the preequilibrium cluster emission in the transfer reaction- s. The article is organized as follows. In Section II we give a brief description of the DNS model for describing the preequilibrium cluster production.

In Section III, the production cross sections, kinetic energy spectra and angular distributions of the preequilibrium clusters are analyzed and discussed. Summary and perspective are shown in Section IV.

II. BRIEF DESCRIPTION OF THE MODEL The dinuclear system (DNS) model was first proposed by Volkov [ ] to describe the deep inelastic heavy ion collisions. Adamian et al. applied the DNS model to fu- sion evaporation reactions in competition with the quasi- fission process to study the synthesis of superheavy nuclei for the first time [ ]. The Lanzhou nuclear physic- s group has further developed the DNS model [ e.g., introduced the barrier distribution function method in the capture process, considered the effects of quasi- fission and fission in the fusion stage, used statistical e- vaporation theory and Bohr-Wheeler formula to calcu- late the survival probability of superheavy nucleus. The DNS model has been used widely to study the produc- tion cross section, quasi-fission, fusion dynamics etc. in the synthesis of superheavy nucleus based on fusion e- vaporation (FE) reactions and the multinucleon transfer (MNT) reactions [ With the DNS model, we have calculated the tempo- ral evolution, the kinetic energy spectra and the angu- lar distributions of the pre-equilibrium clusters in trans- fer reactions with the incident energy near the Coulomb barrier. Compared to our previous work [ ], we have introduced the transfer of clusters in the master equa- tion of the DNS model, and the Coulomb force is consid- ered in the pre-equilibrium cluster emission process. The pre-equilibrium particle is formed before the compound nucleus formation, and its emission continues until the

composite nucleus is formed. The cross section of pre- equilibrium particle emission ( ν = n, p, d, t , 3 He, α , 6 , 7 Li and 8 , 9 Be) is defined as

N 1 = N ν π λ 2 (2 J + 1) ∫ f ( B )

σ ν ( E k , θ, t )=

Z 1 = Z ν

, J, B , t, B Here, are the kinetic energy and emission angle of the particles when they are ejected from the projectile-like or target-like fragments, is the time of the reaction process. The reduced de Broglie wavelength , and , t, B ) de- notes the realization probability of the DNS fragment ) is the emission probability of the pre-equilibrium particles. is the excitation en- ergy for the fragment ( ), which is associated with the center-of-mass energy and incident angular mo- mentum The maximal angular momentum taken to be the grazing collision of two colliding nuclei.

The DNS fragments ( ) ranging from the light one ) to the composite system ( ), with being the total proton and neutron numbers, respectively. 2.1 The capture cross section of binary system overcoming the Coulomb barrier In the capture stage, the collision system overcomes the Coulomb barrier to form a composite system. The capture cross section is given by

σ cap ( E c.m. ) = π λ 2 ∑ J max J =0 (2 J + 1)

, J, B where , J, B ) is the penetration probability over- coming the barrier For the light and medi- um systems, , J, B ) is calculated by the well- known Hill-Wheeler formula [ , J, B being the width of the parabolic barrier at ). Due to the effect of multidimensional quantum penetration, the Coulomb barrier appears a distribution. By introducing a barrier distribution function based on the original Hill- Wheeler formula [ ], the penetration probability can be written as

T ( E c . m . , J ) = ∫ f ( B )

1 + exp ) being the width of the parabolic barrier at

For the heavy systems, the collision system does not form a potential energy pocket after overcoming the Coulomb barrier, ) is calculated by the clas- sic trajectory method,

T ( E c.m. , J ) =

The reduced mass is ) with being the nucleon mass and the mass number- s of projectile and target nuclei, respectively. denotes the Coulomb radius, and ) with 5 fm.

The barrier distribution function is Gaussian form [

f ( B ) = 1

N exp

dP ( Z 1 , N 1 , E 1 , β 1 , B, t ) dt = ∑

And in the equation, is the mean transition probability from the channel ( The quantity indicates the microscopic dimension corresponding to the macroscopic state ( ). In this process, the transfer of nu- cleons or clusters is satisfied with the relationships, , each represents the transfer of a neutron, proton, deuteron, tritium, . Note that we ignored the quasi-fission of DNS and the fission of heavy fragments in the dissipation process. The ini- tial probabilities of projectile and target nuclei are set to = 0) = = 0) = 0

5. The nucleon transfer process satisfies the

unitary condition ) = 1. The normalization constant satisfies = 1. The quantities and ∆are evaluated by 2 and ∆= ( 2, respectively. is the Coulomb barrier at waist-to-waist orientation and is the minimum barrier by varying the quadrupole deformation of the colliding partners. Here we take as the Coulomb barrier at tip-to-tip orientation. 2.2 The nucleon and cluster transfer dynamics In the nucleon transfer process, the distribution prob- ability of the DNS fragments is obtained by numerically solving a set of master equations [ ]. Fragment ( has the proton number of , the neutron number of the internal excitation energy of , and the quadrupole deformation , and the time evolution equation of its distribution probability can be described as

Similar to the cascade transfer of nucleons [ 22 ], the transfer of clusters is also described by the single-particle Hamiltonian,

H ( t ) = H 0 ( t ) + V ( t ) . (7)

Single-particle states are defined with respect to the cen- ters of the interacting nuclei and are assumed to be or- thogonalized in the overlap region. Thus, the annihila- tion and creation operators depend on the reaction time.

The total single particle energy is

H 0 ( t )= ∑

, B, t , B, t , B, t , B, t , B, t , B, t , B, t , B, t , B, t , B, t , B, t , B, t

The interaction potential is

V ( t )= ∑

The quantity represents the single-particle energies, is the interaction matrix elements, parame- terized to the following form:

u α K ,β ′ K = U K,K ′ ( t ) (10)

here, the calculation of the ) and ) have been described in Ref. [ In the relaxation process of the relative motion, the DNS will be excited by the dissipation of the relative ki- netic energy and angular momentum. The excited DNS opens a valence space in which the valence nucleons have a symmetrical distribution around the Fermi surface.

Only the particles at the states within the valence space are actively excited and undergo transfer. The averages on these quantities are performed in the valence space as follows:

∆ ε K =

here, the symbol is the local excitation energy of the DNS fragments, which provides the excitation energy for the mean transition probability. The number of valence states in the valence space is is the sin- gle particle level density around the Fermi surface. The number of valence nucleon is . The micro- scopic dimension for the fragment ( ) is evaluated

d ( m 1 , m 2 ) = ( N 1 m 1

The mean transition probability is related with the local excitation energy and the transfer of nucleons or clusters, and it can be microscopically derived from the interaction potential in valence space as represents the spin-isospin statistical factors, and we use the winger density approach to identify particle types ], i.e. 96 for neutron, proton, deuteron, tritium, , respectively. It is no- ticed that the cluster transition probability is related to the cluster formation probability with the cluster struc- ture, cluster potential, cluster binding energy, Mott effec- t etc. More improvements are still needed in the future work.

The memory time is connected with the internal exci- tation energy [

< V KK V ∗ KK ′ > = 1

The interaction matrix elements are calculated by in which with the states ) and In the relaxation process of the relative motion, the DNS will be excited by the dissipation of the relative kinetic energy. The local excitation energy is determined by the dissipation energy from the relative motion and the potential energy surface of the DNS [

ε ∗ ( t ) = E diss ( t ) − ( U ( { α } ) − U ( { α EN } )) . (18)

where , J, R, β the projectile-target system. The excitation energy of the DNS fragment( denotes the interaction time, which is associated with the reaction system and the relative angular momentum, and can be gained by the deflection function [ ]. The energy dissipated into the DNS is

E diss ( t ) = E c.m. − B −⟨ J ( t ) ⟩ ( ⟨ J ( t ) ⟩ + 1) ℏ 2

And the radial energy is

⟨ E rad ( J, t ) ⟩ = E rad ( J, 0) exp( − t/τ r ) , (20)

with the relaxation time of radial motion being s, the initial radial energy being ). The dissipation of the relative angular momentum is described by

⟨ J ( t ) ⟩ = J st + ( J i − J st ) exp( − t/τ J ) (21)

The angular momentum at the sticking limit is J st = J i ζ rel /ζ tot and the relaxation time τ J = 15 × 10 − 22 s. The

are the relative and total moments of inertia of the DNS, respectively. The initial angular momentum is set to be in Eq. (1). The relaxation time of ra- dial kinetic energy and angular momentum is associated with the friction coefficients in the binary collisions. The values in this work are taken from the empirical analysis in deeply inelastic heavy-ion collisions [ The potential energy surface (PES) of the DNS is e- valuated as with the relationship of The symbol denotes the quantities , J, R, β . In the calculation, the distance between the centers of the two fragments is chosen to be the value at the touching configura- tion, in which the DNS is assumed to be formed, and ) with 3 fm. 2) and ) are the negative binding energies of the fragment ( ) and the com- pound nucleus ( ), respectively. The represent the quadrupole deformations of the two fragments at ground state, and 2) denote the angles between the colli- sion orientations and the symmetry axes of deformed nu- clei. The interaction potential between fragment ( and ( ) is derived from where is the Coulomb potential using the Wong for- mula [ is the nucleus-nucleus potential using the double folding potential [ ], and ) denotes the deformation energy of the DNS at reaction time t,

V def ( t ) = 1

2 C

The quantity 2) denote the stiffness parameters of the nuclear surface, which are calculated by the liq- uid drop model [ ]. Detailed calculations of ) can be obtained from Ref. [ ] and the references therein.

Shown in Fig. 1 [FIGURE:1] is the PES in collisions of Pt. The zigzag lines are the driving poten- tials, which are estimated by the minimal PES values in the process of transferring nucleons. The incident point is denoted by the star symbol.

2.3 The preequilibrium cluster emission

The emission probabilities of pre-equilibrium clusters with the kinetic energy are calculated by the uncer- tainty principle within the time step

P ν ( Z ν , N ν , E k ) = △ t Γ ν / ℏ . (25)

Here the time step is set to be s for the reactions induced by C and N, but for the reactions induced by Ni isotopes.

Based on the Weisskopf evaporation theory [ ], we have the particle decay widths as follows, ) = (2 being the spin, mass and binding energy of the evaporating particles, respectively.

The inverse cross section is given by

σ inv = πR 2 ν T ( ν ) , (27)

with the radius of

R ν = 1 . 21 [ ( A − A ν ) 1 / 3 + A 1 / 3 ν ] . (28)

The penetration probability is set to be ) = 1 for neutron and ) = [1 + exp(2 charged particles with = 5 MeV and 8 MeV for hy- drogen isotopes and other charged particles, respectively.

It should be mentioned that the local equilibrium of the DNS is assumed to be formed and the excitation energy for the th fragment is associated with the local excitation energy with the mass table [ The level density is calculated from the Fermi-gas mod- el as

ρ ( E ∗ , J )= 2 J + 1 24 √

with σ 2 = 6 ¯ m 2 √

and ¯ . The pairing correction energy is set to be 12 0 and for even-even, even-odd and odd-odd nuclei, respectively. The level density parameter is related to the shell correction energy ) and the excitation energy of the nucleus as , Z, N ) = ˜ )[1 + The asymptotic Fermi-gas value of the level density pa- rameter at high excitation energy is ˜ , and the shell damping factor is given by ) = 1 ) with ). The pa- rameters are taken to be 0.114, 0.098, 1. and 0.4, respectively [ The kinetic energy of the pre-equilibrium particle is sampled by the Monte Carlo method within the energy range ) and Here, represents the Coulomb force that the outgoing particles need to overcome, and for neutron,

Watt spectrum is used for the neutron emission [ ] and expressed as

dN n dϵ n = C n ϵ 1 / 2 n T 3 / 2 w exp ( − ϵ n T w

with T w = 1 . 7 ± 0 . 1 MeV and normalization constant C n .

For the charged particles, the Boltzmann distribution is taken into account as

dN ν dE k = 8 πϵ ν

with the mass m ν and local temperature T ν = √

E ∗ /a , and a = A/ 8 being the level density parameter.

We use the deflection function method [ 38 , 49 ] to calcu- late the angular distribution of the pre-equilibrium par- ticles emitted from the DNS fragments as

Θ( J i ) = Θ C ( J i ) + Θ N ( J i ) . (33)

The Coulomb deflection is given by the Rutherford func- tion as

Θ( J i ) C = 2 arctan Z p Z t e 2

2 E

with the incident energy and impact parameter The nuclear deflection is calculated by

Θ( J i ) N = − β Θ gr C ( J i ) J i J gr

Here Θ ) is the Coulomb scattering angle at the grazing angular momentum . The quantity is the incident angular mo- mentum, is the reduced mass of the collision system, ) denotes the interaction potential with being the Coulomb radius. The parameters parameterized by fitting the deep inelastic scattering in massive collisions as ) + 15 36 exp( ) + 0 117 exp(

f ( η ) = [1 + exp η − 235 32 ] − 1 . (38)

The quantity η = Z 1 Z 2 e 2

, is the Sommerfeld param- eter, and the relative velocity is calculated by . For the th DNS fragment, the emission angle is determined by

Θ i ( J i ) = Θ( J i ) ξ i ( ξ 1 + ξ 2 ) (39)

with the moment of inertia for the th fragment. III. RESULTS AND DISCUSSION The pre-equilibrium cluster emission in the transfer reaction is very complicated, which is not only related to the structure of the collision system e.g. the pre- formation factor, but also related to the dynamic evolu- tion of the reaction process, i.e. the dissipation of relative motion and the coupling of internal degrees of freedom of The potential energy surfaces in the reactions of (a) Bi and (b) Pt, respectively.

reaction system. The emission of preequilibrium cluster is a non-equilibrium process of time and space evolution, which is a powerful probe for deeply investigating the MNT reaction dynamics.

The temporal evolution of the emission probability of n, p, d, t, He and from the transfer reactions of Ta and Au at = 115 MeV is shown in Fig. 2 [FIGURE:2] and Fig. 3 [FIGURE:3], respectively. It is noticed that the formation of the compound nucleus is the or- der of a few of hundred zeptoseconds, while the reaction time of preequilibrium process is about several zeptosec- onds. It can be seen from the figures that the emission of preequilibrium cluster continues until the formation of the composite nucleus. At the beginning of the reac- tion, the emission probability of the preequilibrium clus- ter increases rapidly, reaching a maximum value at about s, and then remaining stable or decreasing gradually. The emission probabilities of and hydrogen isotopes are comparable, and the yields are about 3 orders of magnitude lower than that of neutrons, but much larger than that of He. The local excitation energy of the DNS fragment increases with time, and the emit- ted clusters could take away a part of the energy, which is conducive to the formation of compound nucleus with the lower excitation energy. The total emission cross sec- tions of the preequilibrium clusters can be obtained by counting the temporal evolution of cluster yields. The total emission cross sections of different preequilibrium particles are shown in Table . It is obvious that the yields are comparable with the proton emission Shown in Fig. 4 [FIGURE:4] is the kinetic energy spectra of the light nucleus produced in the transfer reactions of Ta at E =115 MeV. It can be seen from the figure that the kinetic energy spectra of different reactions show the similar shape, presenting the Boltz- mann distribution. The emission of neutron is the most important. Compared with the previous work [ ], we have introduced the Coulomb barrier correction in this work. Hydrogen isotopes have similar emission probabil- ities due to the same amount of charge, and the peak of their kinetic energy spectrum is about 10 MeV. Due to He are more charged, the kinetic energy spectra move in the direction of greater energy (i.e. move to the right in the picture). Besides, we can see from Fig. 4 that the emission probability of is about three to five orders of magnitude higher than He, for the reason that the former has lower separation energy and is more easy to be emitted from the DNS fragments. The above calcu- lation results are consistent with the experimental data In the Fig. 5 [FIGURE:5], we exhibit the kinetic energy spectra of the pre-equilibrium clusters (n, p, d, t, Be) in the transfer reactions induced by C and the same target nucleus Bi. The kinetic energy spec- tra of these pre-equilibrium particles in the transfer reac- tions show the nuclear structure effect and the dynamic characteristics of nuclear reaction. The available experi- mental data for the emission from HIRFL for the mas- sive transfer reaction of ] and from RIKEN ] are nicely reproduced with the DNS model.

The excitation energy of DNS fragments, and transition probability, binding energy and separation en- ergy of transferred nucleons (clusters) affect the kinetic energy spectra. The emission cross section of preequi- librium cluster is mainly related to its formation proba- bility and emission probability. In our calculation, it is assumed that the clusters already exist in the DNS, so the emission cross sections of different clusters are mainly determined by the emission probabilities. The higher the charge of the emitted particle, the higher the Coulomb barrier. On the other hand, the larger the separation en- ergy of the cluster, the smaller the decay width and the lower emission probability. The kinetic energy spectra of clusters are strongly related to the Coulomb barriers and excitation energies of composite system.

The emission of the preequilibrium cluster is not only related to the reaction system, but also to the incident energy. Shown in Fig. 6 [FIGURE:6] is the comparison of the time evolution and the kinetic energy distribution of the trans- fer reaction, Pt, at the different incident energy of 220 MeV and 240 MeV. The left part of this figure is the temporal evolution, and the right is the kinetic ener- gy spectra of the pre-equilibrium particles. The kinetic energy of pre-equilibrium cluster is mainly determined by the local excitation energy of projectile-like and target- like fragments, and high local excitation energy is benefi- cial to the cluster emission. We can see that the emission probability at E = 240 MeV is about 2 to 3 orders of magnitude higher than at E = 220 MeV, indicat- ing that the emission probability of the pre-equilibrium clusters increases with the incident energy. In Fig. 7 [FIGURE:7], we compare the transfer reactions of bombarding the tar- get nucleus Pt with heavier isotopes of Ni at E 240 MeV, on the left is the kinetic energy spectra of the pre-equilibrium clusters emitted in the Pt reac- tion, and on the right is the reaction of Pt. It can be found that compared to the reaction system of Pt, the reaction induced by Ni seems to be more likely to emit neutrons, but the former is more like- ly to emit protons.

In the both reaction systems, the peak of the kinetic energy spectra of proton isotopes is about 9 MeV, while the peak of kinetic energy spectra is about 17 MeV.

The particles emitted in the preequilibrium process and from the compound nucleus have different kinetic energy and angular distributions [ Direct particles primarily emit in the same direction as incident particles and have similar energy to each other, while the particles of the compound process emit in all directions, in equal amounts forward and backward. Preequilibrium particles tend to be emitted forward and are generally more en- ergetic than those from the composite nucleus. Shown

Temporal evolution of the preequilibrium cluster emission in the reactions of (a) Tb and (b) at the beam energy of 115 MeV.

The same as in Fig. 2, but for the collisions of Ta and Au, respectively.

TABLE I. Production cross sections of neutron, proton, deuteron, triton, He and in the preequilibrium process of massive transfer reactions. reaction system (MeV)

72 Ni+

e x p : q = 6 8 . 2 �

in Fig. 8 [FIGURE:8] is the angular distributions of the emitted pre-equilibrium clusters in Pt at E MeV. The angular distribution is different for differen- t reaction systems. For the same reaction system, the shape of the angular distributions of different clusters are quite similar, because different clusters may be evaporat- ed from the same excited DNS fragment. It can also be seen from the figure that the angular distributions of the pre-equilibrium particles are anisotropic, and their shape shows the similar characteristics as the angular distribu- tions of fragments in the multinucleon transfer reactions ]. In the program calculation, we ignored the val- ues where the output was less than 1

10. Under the

three reaction systems, the angular distributions of the

= 1 1 5 M e V ( c )

particles increase rapidly when the angle of the center of mass system is about 26 o , and reach the maximum value between 32 o and 36 o . There exhibits a window with 32 o - 160 o for the pre-equilibrium neutron emission. The study of the angular distribution of pre-equilibrium clusters in the transfer reaction is of great significance to the study of the angular distribution of the primary fragments in the MNT reaction, and is helpful for the management of the experimental measurements.

Kinetic energy spectra of the light nuclei produced in the reactions of (a) Tb, (b) Tm and (c) Ta at =115 MeV, respectively.

Kinetic energy spectra of the preequilibrium clusters produced in collisions of (a) Bi at E =73 MeV and (b) Bi at E =115 MeV, respectively. The available experimental data ( particle) are shown for comparison from HIRFL for the reaction of ] (left panel) and from RIKEN for ](right panel), respectively.

IV. CONCLUSIONS In summary, within the framework of the DNS mod- el, we have investigated the emission mechanism of the preequilibrium clusters in the massive transfer reactions near Coulomb barrier energies, i.e., the temporal evolu- tion, the kinetic energy spectra and the angular distri- butions of n, p, d, t, Be in collisions Pt. The cluster transfer and dynamic deformation coupled to the relative dissipation of angu- lar momentum and motion energy in the DNS model.

The emission of the preequilibrium clusters strongly de- pends on the incident energy, the separation energy and the Coulomb barrier from the primordial DNS fragments.

The yields of hydrogen isotopes and α production have the similar magnitude, but more probable than the heavy particles. The kinetic energy spectra manifest the differ- ence of charged particles, i.e., the more kinetic energy for the α emission than the ones of protons. The preequi- librium clusters follows the MNT fragment emission on the angular distributions and related to the correlation of nucleons. The reaction mechanism is helpful for investi- gating the cluster structure of atomic nucleus and MNT

(a) The temporal evolution and (b) kinetic energy spectra of the preequilibrium clusters produced in collisions of Pt at E =220 MeV and E =240 MeV, respectively.

Kinetic energy spectra of the preequilibrium clusters produced in collisions of Pt at E =240 MeV.

fragment formation, i.e., the yields, shell effect, emission dynamics etc, which is being planned for the forthcoming experiments at HIAF in Huizhou.

ACKNOWLEDGEMENTS This work was supported by the National Natural Sci- ence Foundation of China (Projects No. 12175072 and No. 12311540139).

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