1. Testing isospin-symmetry breaking and mapping the proton drip-line with Lanzhou facilities Yang Sun Shanghai Jiao Tong University, China SIAP, Jan.10, 2013

2. Formalism first applied to nuclei by Heisenberg W. Heisenberg, Z. Phys. 77 (1932) 1 The name `isotopic spin’ first given by Wigner E. Wigner, Phys. Rev. 51 (1937) 106 Isospin of a nucleon: Projection of isospin: neutron proton Total isospin projection: Total isospin: The concept of isospin

3. Isospin is only an approximate symmetry Phys. Rev. 51 (1937) 106 Classify different nuclear states having same quantum numbers 51 Fe: N=25, Z=26,T z =-1/2 51 Mn: N=26, Z=25,T z =1/2 Isospin symmetry Warner et al., Nature Phys. 2 (2006) 311

4. Suppose attractive nucleon-nucleon interaction is v Charge symmetry: v nn = v pp Charge independence: v np = (v nn + v pp ) / 2 Scattering data show that both symmetries are broken R. Machleidt, Phsy. Rev. C 63 (2001) 034005 Nuclei are strongly correlated many-systems, having two most important properties: Strong spin-orbit interaction Shape effects and collective motion The effects can be enhanced in heavier nuclei. Isospin-symmetry breaking

5. This can be easily derived : Let H CI be charge-independent Hamiltonian, is its eigenstate. H’ CV is charge-violating interaction Assuming two-body interactions: Isospin-symmetry breaking

6. Taking H’ CV as perturbation One obtains the famous Isobaric Multiplet Mass Equation (IMME): which depends on T z up to the quadratic term. Isospin-symmetry breaking

7. Higher orders of T z (dT z 3, eT z 4,…) in IMME are possible, due to Higher order perturbation Effective three-body forces Any other complicated structure effects such as: shape coexistence shape phase transition Isospin-symmetry breaking

8. IMME has been tested up to A~40

9. Tz=-1/2, ( 78 Kr Beam) Tz= -1, -3/2, ( 58 Ni Beam) Experiment in Lanzhou

10. Some short-lived N<Z masses have never been measured. They lie near the proton drip-line and are very exotic. These masses so far have been calculated using the best knowledge in nuclear structure models. The new mass measurement can serve as a good testing ground. Interest in physics: Measured masses connecting even-even N=Z waiting point nuclei, important for understanding the rp nucleosynthesis process. Testing the isobaric multiplet mass equation (IMME). Understanding the Coulomb Displacement Energy (CDE) for mirror nuclei in deformed and unbound regions. Mass measurement in Lanzhou

11. Wigner et al. (1957), by assuming the two-body nature for any charge-dependent effects and the Coulomb force between the nucleons, noted that masses m of the 2T+1 members of an isobaric multiplet are related by the isobaric multiplet mass equation (IMME): Large deviation of IMME at A~53 ME=mass excess Large deviation for A=53, T=3/2 quartet. A non-zero d term is needed. Y.-H. Zhang et al PRL (2012)

12. Difference in binding energy of mirror nuclei Binding energy of the proton-rich nucleus Binding energy of the neutron-rich nucleus D(A,T) calculated with Skyrme Hartreee-Fock method Coulomb displacement energy (CDE)

13. A more sensitive plot: the difference in CDE Results show the well-known odd-even staggering, but find anomaly near A~70: the staggering changes phase! Anomaly in CDE at A~70 ? Odd-even staggering explained by E. Feenberg and G. Goertzel, Phys. Rev. 70 (1946) 597 ?

14. Comparison of calculated CDE (A. Brown, K. Kaneko) with measurement shows large deviation at A~70. Are these deviations due to deformation effects? Anomaly in CDE at A~70

15. In these nuclei, different shapes are known to co- exist near ground state. Nuclear shape coexistence leads to shape isomeric states (excited states having relatively long lifetimes). One can question the HF method for calculation of CDE. Question of shape effect

16. 吸积盘

17. The charge-dependent and isospin nonconserving forces are considered: V’ CV V C : Coulomb interaction H’ sp : Coulomb single-particle interaction including shifts due to electromagnetic spin-orbit interaction The last term: fp and fpg shell model calculations

18. Comparison of calculated difference in CDE with GXPF1A and JUN45 forces with A. Brown calculation and measurement. Theory or exp problem?

19. Comparison of calculated CDE (by A. Brown) with measurement shows large deviation at A~70. Mapping the proton drip-line GXPF1A JUN45 For odd-mass nuclei, T=1/2,3/2,5/2 Calculation of 1-proton and 2-proton separation energy For even-mass nuclei, T=1,2,3

20. The first PRL of X. Tu et al., through the 65 As mass concluded that 64 Ge is not a good waiting-point nucleus. Precise mass measurement for 69 Br which can determine the waiting-point property for 68 Se. Precise mass measurement for 73 Rb which can determine the waiting-point property for 72 Kr. Improved mass data for upper fp-shell nuclei. Test the predicted proton drip-line by the current calculations by using the CDE method. Excited states and spectra of these exotic nuclei. Important questions: Can Lanzhou mass measurement answer?

21. The mass experiment at Lanzhou CSRe successfully measured some short lived N<Z nuclei near the proton drip-line. The measured masses test existing nuclear models for nuclear masses and arise questions in fundamental physics. The new mass measurements allow us to think of the fundamental questions in isospin-symmetry breaking in the upper fp-shell for the first time. The mass measurement and the CDE study allow to map the proton drip-line, and have impact on the study of nucleosynthesis in the rp-processs. Summary