Unified fission model for proton emission

The unified fission model (UFM) combining with the phenomenological assault frequency has been carried out to investigate the proton-radioactivity half-lives of spherical proton emitters. The results are in good agreement with the experimental data and other theoretical values, and newly observed spherical proton emitters have been analyzed. Finally, the effect of angular momentum transfer on half-life of proton emission has been discussed in detail and a formula can be used to describe this relationship.     

Theoretical Calculation for Half-Lives of Spherical Proton Emitters

Half-lives of the proton radioactivity for spherical proton emitters are investigated theoretically in the Wentzel- Kramers-Brillouin approximation. Microscopic proton-nucleus interaction potentials are obtained by folding the densities of the residual daughter nuclei with renormalized M3Y effective interactions. We also take the spectroscopic factor （Sp） into account in the calculation, which is evaluated in the relativistic mean field approach using the force NL3. The calculated results are found to be in good agreement with the experimental data.     

Unified fission model for proton emission

The unified fission model （UFM） combining with the phenomenological assault frequency has been carried out to investigate the proton-radioactivity half-lives of spherical proton emitters. The results are in good agreement with the experimental data and other theoretical values, and newly observed spherical proton emitters have been analyzed. Finally, the effect of angular momentum transfer on half-life of proton emission has been discussed in detail and a formula can be used to describe this relationship.     

Empirical formulas for proton decay half-lives:Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental Q values.     

Proton radioactivity within the generalized liquid drop model with various versions of proximity potentials

In the present work, we systematically investigate the proton radioactivity half-lives of spherical proton emitters adopting a generalized liquid drop model(GLDM) with 16 different proximity potentials, of which the proximity potential Prox.77-13 gives the closest results to the experimental data. Combined with the previous conclusion that the GLDM with proximity potential Prox.77-13 can also best describe α decay half-lives, which makes the model more uniform and consistent.Further, we use the proximity potential Prox.77-13 in GLDM to predict the proton radioactivity half-lives of 14 spherical proton emitters that are allowed energetically but not yet observed experimentally or specifically quantified. Finally, we research the Geiger-Nuttall law for proton radioactivity. The results reveal that the Geiger-Nuttall law can also be well used to study the proton radioactivity half-lives of isotopes with the same orbital angular momentum l.     

A formula for half-life of proton radioactivity

We present a formula for proton radioactivity half-lives of spherical proton emitters with the inclusion of the spectroscopic factor. The coefficients in the formula are calibrated with the available experimental data. As an input to calculate the half-life, the spectroscopic factor that characterizes the important information on nuclear structure should be obtained with a nuclear many-body approach. This formula is found to work quite well, and in better agreement with experimental measurements than other theoretical models. Therefore, it can be used as a powerful tool in the investigation of proton emission, in particular for experimentalists.     

Excited states in128Ba

A group of proton emitters of Au, Ir, Re, Ta has been identified by means of mass values derived from the experimental data. The proton drip line has been determined. It is shown that on the boundary of the proton stability the values of proton pairing energies increase by about 50% as compared with the isotone nuclei near the betastability line.     

Proton emission from the drip-line nuclei I-Bi using the WKB approximation with relativistic mean-field densities

crucial application to the existence of exotic nuclei. The effective relativistic meanfield formalism(E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin(WKB)barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated halflives are in good agreement with the experimental results for all emitters considered in this study.     

Theoretical study on spherical proton emission

The proton radioactivity half-lives of spherical proton emitters are investigated within a generalized liquid drop model(GLDM),including the proximity effects between nuclei in a neck and the mass and charge asymmetry.The penetrability is calculated in the WKB approximation and the assault frequency is estimated by the quantum mechanism method considering the structure of the parent nucleus.The spectroscopic factor is taken into account in half-life calculation,which is obtained by employing the relativisti...     

滴线核的质子发射

质子放射性是极端丰质子核的一个重要性质 .球形核的质子发射用 WKB方法可以很好地描述 ,变形核的质子发射则须解耦合道的薛定谔方程 .通过140Ho和141Ho质子发射体的研究可给出非束缚 Nilsson轨道的结构信息.Proton emission is a very important property of the extreme proton rich nuclei. It is introduced that the proton emission from a spherical nucleus can be well described by WKB method, while that from a deformed nucleus must be described by means of solving coupled channel Schrdinger equations. The investigation of the proton emitters 140Ho, 141Ho offered information about the structure of unbound Nilsson orbitals.     

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     

Systematics of proton emission

A very simple formula is presented that relates the logarithm of the half-life, corrected by the centrifugal barrier, with the Coulomb parameter in proton decay processes. The corresponding experimental data lie on two straight lines which appear as a result of a sudden change in the nuclear shape marking two regions of deformation independently of the angular momentum of the outgoing proton. This feature provides a powerful tool to assign experimentally quantum numbers in proton emitters.     

Proton radioactivity with analytically solvable potential

The phenomenon of proton emission is treated as a process of asymmetric fission through a one-dimensional potential barrier developed due to combined effects of the Coulomb potential, centrifugal potential and various renormalization processes. The barrier is simulated to an asymmetric, smooth and analytically solvable potential with adjustable depth, shape and range. The half-lives of proton emitters in the mass range A = 105–171 have been calculated using exact expression for the transmission coefficients. Good agreement with the experimental data is obtained by the adjustment of just one parameter in all the cases.      

The single-particle characteristics of Pb isotopes near the drip lines calculated within the dispersive optical model

The neutron and proton dispersive optical potential for the ²⁰⁸Pb nucleus has been determined for the energy region from–70 to +60 MeV and used to calculate the differential elastic scattering, the total interaction and reaction cross sections, as well as the single-particle characteristics, the neutron and charge densities, rms radii, and the thickness of the nucleus skin. The calculated results are in good agreement with the experimental data. The proton dispersive optical model potential for the spherical and close to spherical Pb isotopes within the neutron and proton drip lines has been obtained by a similar method. The calculation predicts a trend towards the growth of the proton particle-hole gap, which corresponds to Z = 82 shell closure as Z approaches the proton drip line.     

Experimental study for the production cross sections of positron emitters induced from 12C and 16O nuclei by low-energy proton beams

In proton therapy, positron emitters are induced from ¹²C and ¹⁶O nuclei by protons on the beam path in the patient. Many studies for monitoring positron emitters with beam-induced PET technique have been performed by various groups to verify the proton beam range and the dose in the patient for quality assurance (QA). The QA methods proposed by some groups require accurate production cross sections of the positron emitters produced by protons, especially in the low-energy region. The aim of this study was to develop a method for measuring the production cross sections of positron emitters using standard equipment for proton therapy, and to measure the cross sections of positron emitters produced by low-energy protons and verify them in comparison with data of previous experiments. An 80-MeV proton beam was produced by a synchrotron, and the energy was degraded by polyethylene blocks to obtain various beam energies. The number of protons was estimated from the charge induced in a parallel-plate ionization chamber by protons. Low-energy protons of 14–70 MeV were used to bombard ¹²C-rich and ¹⁶O-rich target materials: namely, polyethylene and gelatinous water. The time-activity curve was then measured by a high-sensitivity PET scanner to extract the number of positron emitters produced in the target. The production cross sections for four reaction channels: ¹⁶O(p, pn)¹⁵O, ¹⁶O(p, 3p3n)¹¹C, ¹⁶O(p, 2p2n)¹³N, and ¹²C(p, pn)¹¹C were then measured. The cross sections for the ¹⁶O(p, pn)¹⁵O reaction channel were consistent with data of previous experiments within the uncertainties, while those of ¹²C(p, pn)¹¹C were generally lower than data of previous experiments. These results suggested that further measurements of the production cross sections will be necessary.     

质子放射性寿命的新规律

对球形核和变形核质子放射性的半衰期进行了系统的分析和研究,提出了新的计算质子放射性寿命的解析公式。 通过对公式计算寿命和实验测量值的系统比较,发现两者之间符合得非常好,说明新公式十分准确并具有良好的预言能力。 Systematic calculations on proton radioactivity half lives of both spherical and deformed nuclei are carried out. A new formula with only four parameters is proposed for proton radioactivity half lives. The half lives calculated by using the new formula are in good agreement with the experimental ones. The new formula is simple but accurate, which is very useful for further experiments.     

偶偶 Ra 同位素的八极形变研究

用反射不对称的相对论平均场理论(RAS-RMF)对偶偶Ra同位素的八极形变进行了系统研究,并与实验数据和有限力程小液滴模型(FRDM)结果进行了比较.结果表明：RAS-RMF理论很好地描述了Ra同位素的基态性质,计算的结合能、双中子分离能和形变与实验数据和FRDM一致.RAS-RMF理论获得的中子、质子密度分布清晰地展现出偶偶Ra同位素由球形逐渐转变为八极形变,到四极形变的过程,与实验观察的八极形变不稳定现象一致.     

Quantitative analysis of proton imaging measurements of laser-induced plasmas

A method for obtaining quantitative information about electric field and charge distributions from proton imaging measurements of laser-induced plasmas is presented. A parameterised charge distribution is used as target plasma. The deflection of a proton beam by the electric field of such a plasma is simulated numerically as well as the resulting proton density, which will be obtained on a screen behind the plasma according to the proton imaging technique. The parameters of the specific charge distributions are delivered by a combination of linear regression and nonlinear fitting of the calculated proton density distribution to the measured optical density of a radiochromic film screen changed by proton exposure. It is shown that superpositions of spherical Gaussian charge distributions as target plasma are sufficient to simulate various structures in proton imaging measurements, which makes this method very flexible.     

偶偶 Ra 同位素的八极形变研究

用反射不对称的相对论平均场理论(RAS-RMF)对偶偶Ra同位素的八极形变进行了系统研究,并与实验数据和有限力程小液滴模型(FRDM)结果进行了比较.结果表明：RAS-RMF理论很好地描述了Ra同位素的基态性质,计算的结合能、双中子分离能和形变与实验数据和FRDM一致.RAS-RMF理论获得的中子、质子密度分布清晰地展现出偶偶Ra同位素由球形逐渐转变为八极形变,到四极形变的过程,与实验观察的八极形变不稳定现象一致. 关键词： 反射不对称平均场(RAS-RMF) 八极形变 偶偶核