Effects Of Shell Correction On Alpha-decay Systematics

For many heavy and super-heavy nuclei,? decay is the key decay mode deter-mining their half-life.Also,it is an important channel for us to acquire information of nuclear structure or to evaluate nuclear models and theories.As is well known,? decay systematics will change abruptly around neutron closure N=126,where many ? decay models give theoretical half-life that deviates largely from experimental one.Aiming to eliminate the systematic deviation,we introduce shell correction into the generalized liquid drop model(GLDM).This work first concentrate on the effect of shape-dependent shell correction after applying Myers' formula in the framework of GLDM.And in the second part,GLDM is modified to fit with the Strutinsky shell correction method.In results analysis section,we emphasize the effect of correction energy as well as its evolution on ? decay sys-tematics.Through both approaches,we observe that shell correction alters the thickness and penetrability of one-body barriers.Since the value of correction energy changes with the number of nucleons,the alteration might differ for different nuclides.This work also compares the ? preformation factors extracted from experimental half-life with those given by the GLDM where the Strutinsky method is applied.And the simi-larity between them is noticed.Lastly,we show that shell correction makes the GLDM accurately reproduce experimental half-life of ? emitters with neutron number N close to 126.And with Strutinsky method,the theoretical half-life of emitters with atomic number Z=52?118 against favored ? decay is improved systematically.And here are the detailed results.In the first part,we discuss what insight the Myers' formula provides us into the shell correction of deformed nuclei.It is shown that apart from the diminishing of shell correction with deformation,the formula also describes the reversal of shell effects ap-pearing with nuclear deformation.Generally speaking,if correction energy is negative for a spherical nucleus,the corresponding penetrability will decrease.Conversely,it will increase slightly if correction energy for a spherical neucleus is positive.To evaluate its effect on half-life,we calculate the root mean sqaure deviation ? between the theoret-ical and experimental halflife in logarithm scale for 157 favored ? decay processes in total.? will decrease from 0.513 to 0.408,about 20 percent better than before.We can thus conclude that shell correction method is valid for ? decay processes:it effectively introduces shell effects into the model,especially around the neutron shell closure 126,significantly improving the accuracy of theoretical half-life.In the next part,the Strutinsky shell correction has been incorporated into the GLDM.Necessary modifications are made to the model.And it turns out that the accu-racy of calculated ? emission half-life is even further improved this way.To solve the single-particle level and obtain the shape-dependent correction energy,we first perform an analytical conversion from asymmetric quasi-molecular shapes into ? parametrized shapes.Then we perform the standard Strutinsky procedure,which is vital for evalu-ating the correction energy.To properly determine the barrier penetrability,we choose deformation parameter to replace the frequently-used mass centre distance.Besides,in the liquid drop picture,we can evaluate ? preformation factors related to one-body bar-rier penetrability.By comparing the factors extracted from experimental data and those given by the inner penetrability,a similarity between them is manifested by taking into account the shell correction,which means the abrupt change of ? decay systematics at N=126 can be reproduced theoretically.Like in the case of applying the Myers' for-mula,the impact of introducing Strutinsky shell correction energy might differ for ?emitters with different neutron numbers.While theoretical half-life increases for nuclei with a neutron number close to 126,in regions far from neutron magic numbers(espe-cially when 130<N<160)half-life will decrease.Overall,the statistical deviations between the calculated and experimental half-life are minimized by the Strutinsky shell correction.For instance,the minimal average absolute deviation and the minimal rms deviation are 0.288 and 0.208,reduced by 22%and 26%respectively.The rms deviation is also better than the one obtained with the Myers'formula.Moreover,these results indicate that the asymmetric shape evolution of ? emitters is important and also that the GLDM can give consistent and reasonable ? preformation factors closely related to the shape evolution processes.In conclusion,shell correction is indispensable for the GLDM or similar nuclear models to reproduce ? decay system-atics.