Probing nuclear bubble configuration by proton induced reaction

TL;DR

This paper investigates how proton-induced reactions can be used to detect bubble configurations in the hypothetical $^{48}$Si nucleus, revealing distinct proton emission patterns that serve as indicators.

Contribution

It introduces a novel method using proton reactions at 0.8 GeV/nucleon to probe nuclear bubble structures, based on transport model simulations.

Findings

More energetic protons emitted along the beam direction with bubble configuration.

Fewer scattered energetic protons at forward angles with bubble configuration.

Proposes a new experimental approach to identify nuclear bubbles.

Abstract

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, nuclear bubble configuration in the hypothetical $^{48}$Si nucleus is studied by proton induced central reaction at an incident beam energy of 0.8 GeV/nucleon. It is found that along the beam direction more energetic protons are emitted with bubble configuration in the target. In the forward angles, compared with the case without bubble configuration, less scattered energetic protons are emitted with bubble configuration in the target. We thus provide a new way to probe the bubble configuration in nuclei.

Full text

The nucleon spatial density distribution is one of the most fundamental characters of atomic nucleus structure. On the account of the nuclear force’s saturation properties, it’s generally considered that a nucleus is commonly compact and the radial locations of neutrons and protons in finite nuclei are in the form of Fermi distributions. However, the density profile could have another atypical forms, such as halo and central depletion, due to the complexity of the nuclear force and quantum many-body system halo1 ; halo2 ; bub1 ; bub2 ; bub3 . The central depletion is vividly called bubble or hollow, which is dependent on the depression range in nuclear density. It has been theoretically discussed that the existence of a bubble structure inside a superheavy nucleus can decrease the total energy of the nucleus bub1 ; bub2 ; bub3 . In fact, the bubble-like structure was first suggested in 1946 bub4 , in which the nucleus was assumed to be a thin spherical shell to explain a series of nuclei with equally spaced energy levels. Two decades afterwards, the spherical bubble nuclei were studied based on liquid drop model (LDM) in 1967 1967 . And later on, the bubble occurrences were extensively explained by utilizing several approaches, such as LDM plus shell correction energy wong , the Hartree-Fock method Campi , the Thomas-Fermi model Saunier as well as transport simulations yong . It is interesting to note that the existence of the bubble structure is not limited to a certain region but a quite extensive region of the nuclear chart light1 ; light2 ; dong1 ; suph1 ; bub1 ; bub2 ; bub3 . And transport simulations show that general excited heavy nuclei may also have central depleted density yong .

It is exciting to see that the first experimental evidence that points to a depletion of the central density of protons in the short-lived nucleus 34Si was provided in 2016 nature2016 . Also in 2016, Najman et al. have recently found some signatures of exotic nuclear configurations such as toroid-shaped objects in 197Au + 197Au reaction at 23 MeV/nucleon Najman .

Using the relativistic Hartree-Fock Lagrangian PKA1, 48Si is predicted to be the first candidate of dual semi-bubble nucleus with both neutron and proton bubble-like shapes long2019 . Since the existence or not of the dual semi-bubble nucleus 48Si can help us to deeply understand the nature of nuclear force, it is very necessary to find an effective way to confirm the dual semi-bubble nucleus 48Si. Of course, our present study based on the bubble nucleus 48Si in proton induced reaction is also, qualitatively or quantitatively, applicable to some other potential bubble or semi-bubble nuclei, such as 34Si, etc.

There are many sensitive probes in heavy-ion collisions to probe nuclear structure and property of both finite nuclei and nuclear matter. Those probes are also considered as an expectation to investigate the bubble configuration. Actually, the visualized probes which can be useful to recognize the novel density profiles have been discussed in recent yeas Bauer ; Gross ; xu ; li ; Cherevko ; yong . In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, the bubble configuration in 48Si is studied in the central p+48Si reaction at 0.8 GeV/nucleon. It is found that in proton induced reaction there are evident effects of bubble configuration on the energetic proton emission in forward angles. The energetic proton emission as a function of scattering angle thus can be a probe of nuclear bubble configuration in the target in proton induced reaction.

The used isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model has evident isospin-dependent nuclear initialization, isospin-dependent nucleon-nucleon cross sections, isospin-dependent single nucleon potential and isospin-dependent Pauli blockings. The used single nucleon potential includes a Skyrme-type parametrization isoscalar term and an exponential isovector term YONG2 . This model has been successfully used to study the bubble configuration of nucleon matter recently yong ; YONG2 . The relativistic Hartree-Fock-Bogoliubov (RHFB) with the PKA1 Lagrangian is one of the most advanced relativistic approaches which is apt at delineating the properties of very neutron-rich nuclei long2019 ; long2 . The dual semi-bubble nucleus 48Si is one possible candidates for double-bubble (both proton and neutron bubble structures) nucleus. For comparison, initializations of the nucleon density distribution in the used transport model adopted two different methods, one uses the general Skrymer-Hartree-Fock (SHF) with Skyrme M* force parameters skm and the other uses the PKA1 Lagrangian long2019 ; long2 .

Fig. 1 shows the density distributions of neutrons and protons as a function of radial co-ordinates in the ground state for 48Si obtained by the two approaches mentioned above. The neutron density is much higher than the proton’s for both of the two cases on account of the great neutron-richness of 48Si. It’s apparently seen that with PKA1 there is a true bubble configuration with a depletion density at the center for both neutrons and protons, while there is a quite compact center for nucleons with the SHF.

The sketch of the reaction with proton as projectile and the bubble nucleus 48Si with density distribution given by PKA1 as target is shown in Fig. 2. It displays the scattering situations in the X-Z profile (Z-axis is the beam direction and X-axis is perpendicular to the Z-axis). The proton is directly projected to the center of 48Si along the Z axis. The depth of color represents the denseness of baryonic density, namely the density of 48Si becomes larger as the color changes from light blue to dark blue. Because of the bubble structure inside 48Si, the reaction should be different from that without bubble in the target. More detailed information about the reaction needs some resultful simulations.

Besides the rough sketch explaining the scattering process physically to some extent, the central p+48Si reaction at a beam energy of 0.8 GeV/nucleon and an impact parameter of 0 fm is simulated based on the framework of the IBUU transport model with density distributions initialized by the SHF (without bubble configuration in the target) and the PKA1 (with bubble configuration in the target). The central collision generally corresponds to the high multiplicity events experimentally. To determine the impact parameter more precisely, the neural network method may be used to select the most central experimental reactions by using the measured values of some observables (such as the multiplicity of charged particles, the transverse and longitudinal momentum distributions of outgoing particles) as the input variables b0fm . Hitting the target 48Si by energetic proton, there should be plenty of emitted protons. The count of emitted protons as a function of kinetic energy detected in the beam direction ($-1^{\circ}\leq\theta\leq 1^{\circ}$, $\theta$ is the angle between emitted direction and the Z axis) in the central p+48Si reaction with and without the bubble configuration is plotted in Fig. 3. To stabilize the result, for each case a million events are accumulated. It is seen that the number of emitting protons with the bubble configuration in the target is evidently larger than that without the bubble configuration in the target, especially for energetic emitting protons. This is because energetic protons are easier to go through the target with the bubble configuration in the target compared with the case without the bubble configuration. From Fig. 3, it is also seen that the effects of the bubble configuration in the target on the energetic emitting protons ($\text{E}_{\text{kin}}\geq$ 600 MeV) can reach 30–40%. Such large effect of the bubble configuration in the target can be detected experimentally.

Although the dual semi-bubble nucleus 48Si is currently hard to produce long2019 , a potential bubble nucleus with similar central depletion density can be an alternative. If they roughly have the same depletion of the central density, the effect of the bubble configuration in the target on the energetic emitting protons should be also similar.

Besides counting energetic emitting protons in the beam direction in proton induced reaction, it is also interesting to see the counts of emitted protons with different scattering angles. Fig. 4 shows the number of emitted energetic protons as a function of scattering angle (relative to the beam direction) in the central p+48Si reaction at 0.8 GeV/nucleon with and without bubble configuration in the target. Each panel has a specific kinetic energy cut. From Fig. 4, it is seen that, in forward angles (especially $10^{\circ}\leq\theta\leq 25^{\circ}$) the number of scattered energetic protons without bubble configuration in the target is larger than the case with the bubble configuration in the target. However, the bubble effect disappears with the increase of the scattering angle. This is because in the forward angle zone, more energetic protons are scattered with compact central density in the target (i.e., without bubble configuration in the target). As the scattering angle increases, the effects of the bubble configuration in the target on the energetic scattered protons decrease due to the small proportion of the bubble area in the whole target. From Fig. 4, it is also seen that the effects of the bubble configuration in the target reach maximum around $\theta=22.5^{\circ}$. Here the specific value of the scattering angle should be decided by the specific size of the bubble and the size of target nucleus.

For scattering energetic protons, the effects of the bubble configuration in the target in proton induced reaction are also decided by the kinetic energy of emitting protons. From panels (a)-(d) in Fig. 4, it is seen that the effects of the bubble configuration on the energetic scattered protons in forward angles reach 16–70% with kinetic energy cuts from E${}_{\text{kin}}>$ 600 MeV to E${}_{\text{kin}}>$ 850 MeV. It shows that very energetic scattering protons in forward angles in proton induced reaction are more suitable to probe the bubble structure in the target. This is because the energetic scattered protons are less affected by the Fermi momentum of nucleons in nucleus thus show more effects of the bubble structure in colliding target.

The present analytical method of the proton induced reaction that is used to probe the bubble configuration in the hypothetical 48Si nucleus can of course be used to probe some other potential bubble or semi-bubble nuclei light1 ; grasso09 ; dug17 . And the proton induced reaction to probe the bubble configuration in nuclei can be considered as an alternative of using the electron scattering experiments to probe nuclear bubble, such as at ELISe@FAIR ec17 or after an upgrade of the SCRIT facility at RIKEN ec18 .

The bubble configuration of atomic nuclei, which is characterized by a depletion of their central density, has been discussed for many decades. The discovery of bubbles in nuclei is an important issue for nuclear structure and nuclear many-body approach. Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, nuclear bubble configuration in the hypothetical 48Si nucleus is studied by proton induced central reaction at an incident beam energy of 0.8 GeV/nucleon. It is found that the emitted protons are much more in the beam direction when the target has a hollow structure than does not have it while in the forward angles (nonzero angles) energetic protons are less scattered when the target has a hollow structure than does not have it. Both effects are enhanced for higher energy proton emission. Angle distribution of the energetic proton emission in the proton induced central reaction at a beam energy of 0.8 GeV/nucleon thus can be a probe of the bubble configuration in target. The present study can also be used to probe some other potential bubble nuclei. Our present results act as a strong motivation to probe some potential bubble nuclei in future proton induced nuclear reaction experiments.

The author XHF thanks Prof. W.H. Long for helpful discussions. This work is supported in part by the National Natural Science Foundation of China under Grant Nos. 11775275, 11435014 and the 973 Program of China (2007CB815004).