Research On The Double Gamow-Taylor Transition Based On The PVPC Mode

In nuclear structure models,the Hartree-Fock and the Hartree-Fock-Bogolyubov methods both start from ansatz waves,by variation reaches energetic minimums,with corresponding wavefunctions considered as intrinsic wavefunctions,and by angular momentum projection,nuclear low-lying states are approximated.The Hartree-Fock method uses a Slater determinant as the ansatz wave,while the Hartree-FockBogolyubov method takes a quasiparticle vacuum as the ansatz wave.We use a general pair condensate as the ansatz wave,which is more general than a Slater determinant,or HFB quasiparticle vacuum,or seniorit-0 state in the general seniority model,for those later three are special cases of a general pair condensate.Therefore,the pair condensate is more general,and should result in energetically lower wavefunctions after angular momentum projection.It is theoretically meaningful to study the variation and angular momentum projection of a pair condensate.Therefore the PVPC model(projection after variation of a pair condensate)is proposed.The Double Gamow-Teller transition(DGT)is a two-nucleon-exchange reaction model of atomic nuclei—two nuclei exchange a pair of protons and a pair of neutrons with each other.The DGT transition operator is constructed with two Gamow-Teller(GT)transition operator,via angular momentum coupling,and the GT operator is constructed with spin and isospin operators,therefore the DGT transition is a spinisospin dynamic process,about two-body correlations in the spin-isospin degree of freedom.The DGT transition and the double beta decay(DBD)are different processes,but recent theoretical efforts reveal possible correlation between transition matrix elements of DGT and DBD.The NUMEN project in Europe is dedicated to measuring the DGT cross sections of Ca-48,in order to shed new light on DBD matrix elements.In Japan,experimental groups at the Osaka university,RIKEN are also making efforts on the double charge-exchange(DCX)reactions.In conclusion,the two nucleon exchange reaction is becoming more important.With a given nuclear initial state,the summation of all transition strengths on different final states is called “non-energy-weighted sum rule”(for convenience,we denote it as “sum rule” hereafter).Sum rules reflect the gross properties of transition strength distributions,for example the Ikeda sum rule of the Gamow-Teller transition results in the discovery of quenching of beta decay.By theoretical study of DGT sum rules,the experimental total strength can be predicted,for reference of experimentalists.Recently theoretical formulas of DGT sum rules have been derived and discussed,but those formulas all need computation results from nuclear models,and there is no systematic investigation of DGT sum rules in a nuclear chart region.On the other hand,the theoretical formulas available are all differences between DGT-strengths and DGT+ strengths,there is no direct computations of DGT-sum rules.In this thesis,we derive new formulas of DGT sum rules in the framework of PVPC,and present systematic calculations of all even-even nuclei in the sd and pf shells.Our computational results show that,when the difference between neutron number and proton number,N-Z,is much larger than one,the DGT-sum rule is approximately only related to N and Z,without significant dependence on the details of the initial wavefunction.But when N ≤ Z,the DGT-sum rule is closly related to the initial wavefunction.According to the theoretical formulas,we subtract GT+ sum rule from the DGT-sum rules of mirror nuclei.We present these systematic results and await for experimental tests.The second part of this theis are a series of new formulas in the framework of PVPC,dedicated to extension the applications of PVPC.The PVPC formulas and codes available up to now are restricted to even-even nuclei,and we derive new formulas for odd-nucleon systems,and the essential formulas for separate projection of protons and neutrons.These work are unfinished,but are important for improvements of the PVPC model.After expanding PVPC to odd-nucleon systems,the number of nuclei applicable would increase by a factor of 4.After expanding PVPC to separate projection of protons and neutrons,the ground state may be lower,and the protons and neutrons can be studied separetely,as in the Projected Shell Model.Therefore,these new formulas are important.In total,the PVPC model has virtues of particle number conservation,clear intrinsic state,and fast for a large number of valence particles.Therefore,the PVPC model is a meaningful increment to the family of methods with variation and angular momentum projection.Because of its good-quality wavefunctions of the parent initial states,the PVPC model is applicable to computations of DGTSR.