Proton Decay in Grand Unified Theories

Interactions which violate the conservation of baryon and lepton number represent an intrinsic part of all grand unified theories (GUTs) of strong and electroweak interactions. These new interactions — predicted within the framework of GUTs — generate B and L violating four-fermion interactions via the exchange of superheavy particles which cannot be ascribed a well-defined baryon or lepton number. The effective coupling constant of these four-fermion interactions might be large enough to make the proton decay detectable by the present generation of experiments. In this review the basic concepts of conventional as well as supersymmetric GUTs relevant for proton decay are sketched. The baryon number violating sector of grand unified theories is discussed in more detail. Special emphasis is laid on the various selection rules arising as consequences of low-energy gauge invariance and supersymmetry for proton decay. These selection rules already determine the coarse pattern of the resulting decay modes and branching ratios without any reference to or detailed knowledge of the underlying grand unified theory. Finally the numerous theoretical predictions are summarized and confronted with experiment.     

Projected Shell Model Description for the Proton Emitters

Proton radioactivity is an important decay mode for nuclei near the proton drip-line. Studies of this decay mode can reveal valuable information on exotic nuclear structure and provide important information on the stucture of nuclei in extreme conditions. The new experimental data can let us understand the interactions in exotic systems, which motivate further theoretical development. The most recent application of the projected shell model (PSM) for proton emitters is represented. We study the rotational bands of the deformed proton emitter 141Ho by using the PSM. The experimental data are well reproduced. Strongly suppressed γ transition from the low-lying IΠ= 3/2+ state makes this state isomeric. Variations in the dynamical moment of inertia are discussed due to band crossings using the band diagram. The calculated results for proton emitter 151Lu shows it is oblately deformed     

Microscopic structure of nuclei from scattering through isobaric analogue resonances

Microscopic nuclear structure information that can be reached by proton scattering through isobaric analogue resonances (IAR) is discussed, mainly within the framework of weak-coupling. The concept of isospin for unbound states is examined. A critical evaluation of the methods for extracting nuclear structure information from the experimental results (such as excitation functions, angular distributions, etc.) is given. The mass regions that are studied in detail are the Pb-region and the N = 82 neutron single-closed shell nuclei. Attention is given to the comparison between weak-coupling calculations and experimental results supporting this concept in many nuclei. Level schemes as well as proton partial decay widths and angular distributions have been calculated and compared with the existing data concerning the proton decay of IAR. The concept of generalized neutron particle-hole (GNPH) state is introduced and its occurence extensively discussed within the Pb-region and N = 82 nuclei.     

Exotic decays of strangelets

The stability of strange matter depends on the implicit assumption that baryon number is conserved. We examine the relevant effective operators which allow strangelets to decay by violating the conservation of baryon number. From the experimental lower limit of 10²⁵ years on the stability of nuclei, we find a lower limit of the order 10⁶ years on the stability of strangelets against such exotic decays.     

Proton Emission——-Recent Results and Future Prospects

Considerable progress has been made in the study of proton-emitting nuclei since the first observation of direct proton emission nearly half a century ago. This has led to improvements in our understanding of this rare decay process and provided invaluable nuclear structure data far from the valley of beta stability. This paper reviews the implications of some recent results for exotic iridium, rhenium and tantalum isotopes and considers prospects for future experimental studies of proton-emitting nuclei located at and above the N =82 neutron shell closure.     

Neutron and proton shell closure in the superheavy region via cluster radioactivity in <Superscript>280–314</Superscript>116 isotopes

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280–314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola-Seaborg-Sobiczewski (VSS) systematic. The plots connecting computed Q values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at N = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at N = 162, 184 and proton shell closure at Z = 114. Our study shows that ₁₆₂²⁷⁶114 is the deformed doubly magic and ₁₈₄²⁹⁸114 is the spherical doubly magic nuclei.      

相对论平均场理论框架下对能的系统研究

在相对论平均场模型的框架内,沿原子核的稳定线,以每隔4个质子或中子提取样本的方法,计算了核谱图上数十个原子核的对能,特别是研究了氧同位素偶-偶核的对能随核子数的变化规律,发现在固定能隙Δ的条件下,对能的大小和核的壳结构有关,由此提出了一种检验闭壳效应的简便方法,进而发现中子数N=6不仅在轻核的丰中子区是一个新幻数,而且在丰质子区也是一个可能的新幻数. 关键词： 相对论平均场模型 对能 能隙 幻数     

有效液滴模型对超铅区结团放射性的研究

利用有效液滴模型计算了超铅区结团放射半衰期.在计算Gamow势垒穿透因子时采用了碎块体积不守恒以及有效惯性系数因子,并用有效的核半径常数公式代替原来的经验公式.理论计算得到的结团放射半衰期和实验值符合得很好,其半衰期对数值的均方差只有0.895.理论结果表明,有效液滴模型能充分反映N=126和Z=82的壳效应,并且在奇数结团25Ne,29Mg中出现了明显的奇偶质量摆动现象.另外,理论计算得到的结团半衰期基本符合盖革-努塔尔定律,并基于理论结果得到了一些关于盖革-努塔尔定律的有意义的结论.     

Observing B-violation in relativistic heavy-ion collisions

Under certain situations, partons formed in heavy-ion collision experiments may expand out forming a shell-like structure. The partons in the outer shell subsequently hadronize, leaving a bubble of pure deconfined vacuum for a first-order quark-hadron phase transition. The bubble collapses and may eventually decay into particles which may thermalize to temperatures exceeding the electroweak transition temperature (100 GeV) at LHC. This will lead to the possibility of unsuppressed electroweak baryon number violating processes.     

Alpha Decay as a Probe of the Structure of Neutron-deficient Nuclei Around Z =82

In this contribution I would like to review briefly our recent studies on nuclear α formation probabilities in heavy nuclei and their indication on the underlying structure of the nuclei involved. In particular, I will show that the empirical α-formation probabilities, which can be extracted from experimental half-lives, exhibit a rather smooth function with changing proton or neutron numbers. This allows us to distinguish the role played by pairing collectivity in the clustering process. The sudden hindrance of the clustering of the nucleons around the N = 126 shell closure is due to the fact that the configuration space does not allow a proper manifestation of the pairing collectivity. The influence of the Z = 82 shell closure on the α formation properties will also be discussed. Moreover, we have evaluated the α-decay fine structure to excited 0+ states in Hg and Rn isotopes as well as the α-decay from the excited 0+ states in the mother nucleus. It is thus found that the α decay is sensitive to the mixture of configurations corresponding to different nuclear shapes.     

基于两势方法系统研究壳结构对原子核α衰变的影响

基于两势方法（two-potential-approach,TPA）系统研究了偶-偶核、奇-A核和奇-奇核α衰变半衰期。为了考虑原子核的壳结构的影响而导致的实验半衰期与计算结果之间的偏差,引入了与α结团形成概率相关的禁戒因子和预形成因子。结合前期相关工作[X.D.Sun et al.,Phys.Rev.C 93,034316（2016）;X.D.Sun et al.,Phys.Rev.C 95,014319（2017）;X.D.Sun et al.,Phys.Rev.C 95,044303（2017）],考虑到壳效应对α粒子预形成的影响,通过分析α衰变半衰期的实验数据,拟合得到了α粒子预形成因子/禁戒因子修正公式的参数,得到了α衰变预形成因子/禁戒因子的计算结果,证实了壳效应及质子-中子相互作用在α结团形成过程中起着重要的作用,离壳越近预形成概率越小离壳越远预形成概率越大。In the present work, the α decay half-lives are systematically studied within the two-potentialapproach for even-even nuclei, odd-A nuclei and odd-odd nuclei. To describe the deviations between experimental half-lives and calculated results due to the nuclear shell structure, α preformation factor and hindrance factor related with α cluster preformation probability are introduced. It is consistent with our previous works[X. D. Sun et al., Phys. Rev. C 93, 034316 (2016); X. D. Sun et al., Phys. Rev. C 95, 014319 (2017); X. D. Sun et al., Phys. Rev. C 95, 044303 (2017)]. Considering the shell effect on the preformation of α and by analyzing the experimental data of the α decay half-lives, the parameters of the α preformation factor/hindrance factor correction formula are obtained. we confirm that the shell effect and the proton-neutron correlation play key roles in the α preformation where the preformation probability near the shell is less than the preformation probability far from the shell.     

Nuclear moments: An effective probe of nuclear stucture

Magnetic dipole and electric quadrupole moments are discussed in nuclei near doubly-closed shell nuclei (the T1 nuclei) and in nuclei along series of single-closed shell nuclei (plus of minus a few nucleons) (the In odd-mass and odd-odd nuclei). We discuss the “additivity” rules for nuclear moments. We also address the EO moment: the liquid drop model and the shell-model are discussed and compared to measurements of nuclear radii in the Ca, Sn and Pb region. In the latter region, the importance of intruder states across the Z=82 proton closed shell is emphasized.     

Shape coexistence around the Z=82 closed shell probed by α-decay

Shape coexistence around the Z=82 closed proton shell, probed via the fine structure in the α-decay of even–even nuclei, is discussed. The power of α-decay studies is demonstrated by presenting the results from a number of decay experiments of Rn isotopes performed at ISOLDE. The total body of experimental evidence on α-decay of even–even nuclei in the Pb region is used to illuminate, through the α-decay reduced widths of the ground state to ground state transitions and through the hindrance factors of the fine structure, the role of multi-particle multi-hole proton excitations across the Z=82 shell. This revised version was published online in July 2006 with corrections to the Cover Date.     

Perspectives from above and beyond the proton drip-line

This paper will review the dramatic increase in our knowledge of one and two proton unbound nuclei [1] such as recoil decay tagging [2] are revealing unique insights into the structure of nuclei beyond the proton drip-line. These studies of excited states provide complementary information to proton radioactivity studies, particularly regarding the role of deformation [3]. Radioactive beams are being used to study two-proton unbound resonances and to study explosive nuclear astrophysical reactions in the region of the proton drip-line.     

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of a-decay is extended to the regions around doubly magic spherical nucleus ^208Pb and around deformed shell closure ^270Hs, respectively. The effects of spherical shell closures (N=126 and Z=82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical a-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus ^208Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state (0^ ) of its deformed daughter nucleus and to the first excited state (2^ ) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus ^270Hs.     

Route to islands of stability of superheavy elements

Problems concerning the existence of hypothetical superheavy elements for which theoretical nuclear models predict high stability with respect to various modes of radioactive decay are discussed. The synthesis of superheavy nuclei and the possibilities for performing experiments aimed at detecting rare events of their production and decay in heavy-ion beams are considered. Experimental results suggesting a considerable increase in the lifetime of nuclei as they approach the closed proton and neutron shells determining the islands of stability of superheavy elements are presented.     

A novel string-derived $Z^\prime$ with stable proton,light neutrinos and R-parity violation

The standard model indicates the realization of grand unified structures in nature, and it can only be viewed as an effective theory below a higher energy cutoff. While the renormalizable standard model forbids proton decay mediating operators due to accidental global symmetries, many extensions of the standard model introduce such dimension 4, 5 and 6 operators. Furthermore, quantum gravity effects are expected to induce proton instability, indicating that the higher energy cutoff scale must be above 10¹⁶ GeV. Quasi-realistic heterotic string models provide the arena to explore how perturbative quantum gravity affects the particle physics phenomenology. An appealing explanation for the proton longevity is provided by the existence of an Abelian gauge symmetry that suppresses the proton decay mediating operators. Additionally, such a low scale U(1) symmetry should feature the following: it should allow for the suppression of the left-handed neutrino masses by a seesaw mechanism; allow for fermion Yukawa couplings to the electroweak Higgs doublets; be anomaly free; and finally be family universal. These requirements render the existence of such U(1) symmetries in quasi-realistic heterotic string models highly non-trivial. We demonstrate the existence of a U(1) symmetry that satisfies all of the above requirements in a class of left–right symmetric heterotic string models in the free fermionic formulation. The existence of the extra in the energy range accessible to future experiments is motivated by the requirement of adequate suppression of proton decay mediation. We further show that, while the extra U(1) forbids dimension 4 baryon number violating operators, it allows dimension 4 lepton number violating operators and R-parity violation.     

Effect of properties of superheavy nuclei on their production and decay

Properties and stability of superheavy nuclei resulting from hot fusion are discussed. It is shown that the microscopic–macroscopic approach allows obtaining the closed proton shell at Z ≥ 120. Isotopic trends of K-isomeric states in superheavy nuclei are predicted. Evaporation residue cross sections in hot fusion reactions are calculated using the predicted properties of superheavy nuclei. Interruption of α decay chains by spontaneous fission is analyzed. Alpha decay chains through isomeric states are considered. Internal level densities in superheavy nuclei are microscopically calculated.     

An Implantation and Detection System for Spectroscopy of 22,24Si

A new decay detection system with high detection efficiency and low detection threshold has been developed for charged-particle decay studies, including -delayed proton, decay or direct proton emission from proton-rich nuclei. The detection system was tested by using the -delayed proton emitter 24Si and was commissioned in the decay study of 22Si produced by projectile fragmentation at the First Radioactive Ion Beam Line in Lanzhou. Under a continuous-beam mode, the isotopes of interest were implanted into two double-sided silicon strip detectors, where the subsequent decays were measured and correlated to the preceding implantations by using position and time information. The system allows to measure protons with energies down to about 200 keV without obvious background in the proton spectrum. Further application of the detection system can be extended to the measurements of -delayed proton decay and the direct proton emission of other exotic proton-rich nuclei.     

Magnetic Field Effect on β^＋ Decay in the Crusts of Accreting Neutron Stars

Based on shell model of nuclei, the influence of a high magnetic field on β^＋ decay in the crusts of accreting neutron stars is analyzed. The magnetic field effect on 54 Mn is discussed. The results show that a weak magnetic field makes little effect on β^＋ decay but a strong magnetic field （B 〉 10^11 G） improves β^＋ decay rates obviously. The conclusion derived will benefit to develop further research on nuclear astrophysics in the future.