Isospin-symmetry breaking in nuclei around the N=Z line
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1 Isospin-symmetry breaking in nuclei around the N=Z line Yang Sun Shanghai Jiao Tong University University of Hong Kong, July. 6-9, 2015
2 The concept of isospin Isospin of a nucleon: Projection of isospin: t 1/ 2 neutron proton t 1/ 2 z t 1/ 2 z Total isospin projection for an A-nucleon system: A T t ( i) ( N Z) / 2 z i 1 z T T, T 1,, T 1, T z is good quantum number, but total isospin T may not.
3 Isospin-symmetry breaking Strong nuclear two-body force is approximately charge symmetric and charge-independent. Charge symmetry: v nn = v pp Invariance under a rotation by 180 o about an axis in isospin space perpendicular to z-direction Charge independence: v np = (v nn + v pp ) / 2 Invariance of any rotation in isospin space Scattering data show that both symmetries are broken R. Machleidt & H. Muether, Phys. Rev. C 63 (2001)
4 Isospin-symmetry breaking Reasons for isospin-symmetry breaking: Coulomb interaction between protons (Nolen Schiffer anomaly) Annu. Rev. Nucl. Sci. 19 (1969) 471 Isospin-nonconserving (INC) nuclear interactions Many-body effects Wigner et al. (1957): Assuming the two-body nature for any charge-dependent effects including the Coulomb force between the nucleons as a perturbation, they noted that mass excess of the 2T+1 members of an isobaric multiplet T are related by the isobaric multiplet mass equation (IMME).
5 Isospin-symmetry breaking It can be easily derived: Let H CI be charge-independent Hamiltonian, eigenstate. H CV is charge-violating perturbation is its Assuming two-body interactions:
6 Isospin-symmetry breaking Taking H CV as a perturbation One obtains the Isobaric Multiplet Mass Equation (IMME): which depends on T z up to the quadratic term.
7 Isospin-symmetry breaking IMME has been tested to be very accurate up to about A~40 M.A. Bentley, S.M. Lenzi, Prog. Part. Nucl. Phys. 59 (2007) 497
8 Isospin-symmetry breaking Isobaric Multiplet Mass Equation (IMME): which depends on T z up to the quadratic term. Higher orders of T z (dt z3, et z4, ) in IMME may be possible, due to Higher order perturbation Effective three-body forces Other many-body effects such as: shape changes W. Benenson, E. Kashy, Rev. Mod. Phys. 51 (1979) 521 Connecting the problem to nuclear many-body effects!
9 Request of advanced facilities All the early tests were for lighter nuclei, where the spinorbit effect (shell effect) is weak. How about heavier nuclei beyond the N=20 shell (the fpshell region and beyond)? Precise mass measurements for A>40, with T= -1/2, T=-1, T= -3/2,... and precise IAS states are very much desired. These nuclei are very short-lived, close to the drip line, and therefore, are very challenging experiments,
10 Storage rings ESR at GSI, Germany HIRFL-CSR at Lanzhou, China
11 Experiment in Lanzhou
12 Deviations from the quadratic IMME New data suggested non-zero T z3 term: + d(a,t)t 3 z Y.-H. Zhang et al, Phys. Rev. Lett. 109 (2012) ME=mass excess Large deviation for A=53, T=3/2 quartet. A non-zero d term is found.
13 Tiny changes in nuclear structure could make it `big in astrophysics The above example shows a tiny value changes in nuclear structure can cause big changes in observations Examples: Rapid proton capture process (rp-process) of nucleosynthesis in nuclear astrophysics Changes in the waiting-point nuclear mass Occurrence of new isomers in waiting point N=Z nuclei
14 rp-process in x-ray burst Neutron star rp-process = Rapid proton capture process One of the major processes for heavy element production Most of the time is spent at the waiting point nuclei
15 abundance slow b decay (waiting point) Tc (43) Mo (42) Nb (41) Zr (40) Y (39) Sr (38) Rb (37) Sb (51) Sn (50) In (49) Cd (48) Ag (47) Pd (46) Rh (45) Ru (44) Kr (36) Br (35) 80 Se (34) 76 As (33) Ge (32) Ga (31) Te (52) Waiting point nuclei Mass number
16 Mass measurement results in Lanzhou These masses are measured for the first time. It confirms that CDE (binding-energy difference between mirror nuclei) method for obtaining unknown masses is reliable at least for 63 Ge, 67 Se. It shows some differences for 65 As and 71 Kr.
17 Abundance of x-ray burst ashes 1s 89% 90% of the reaction flow passes through 64 Ge via proton capture indicating that: 64 Ge is not a significant rp-process waiting point.
18 Probes of isospin-symmetry breaking in nuclei Charge-symmetry breaking Difference between pp and nn interactions (~1%) Experimental signal: Coulomb displacement energy (CDE) -- binding-energy difference between mirror nuclei Charge-independence breaking In T=1 states, pp (T z =-1), np (T z =0), nn (T z =+1) interactions are slightly different Experimental signal: triplet displacement energy (TDE)
19 M.A. Bentley, S.M. Lenzi, Prog. Part. Nucl. Phys. 59 (2007) 497 Questions: Why staggering magnitude in DCDE is greatly reduced for f7/2 shell? Why TDE is significantly larger than the simple Coulomb prediction for f7/2 shell, and drops suddenly at A=58?
20 fp and fpg shell model calculations Kaneko, Sun, Mizusaki, Tazaki, Phys. Rev. Lett. 110 (2013) The charge-dependent and isospin nonconserving (INC) forces are considered: H = H 0 + H INC, H INC in large-scale shell model calculations. H 0 : GXPF1A with full fp shell Honma et al., Eur. Phys. J. A 25 (2005) 499 JUN45 with pf 5/2 g 9/2 model space Honma et al., Phys. Rev. C 80 (2009)
21 fp and fpg shell model calculations The charge-dependent and isospin nonconserving (INC) forces are considered: H = H 0 + H INC, H INC in large-scale shell model calculations. V C : Coulomb interaction H sp : Single-particle interaction including shifts due to electromagnetic spin-orbit interaction The last term: Kaneko, Sun, Mizusaki, Tazaki, Phys. Rev. Lett. 110 (2013)
22 Effect of the INC force for f 7/2 shell D ( A) D( A) D( A 2) 2 Kaneko, Sun, Mizusaki, Tazaki, Phys. Rev. Lett. 110 (2013)
23 Isospin-symmetry breaking in excited nuclear states Nuclei are strongly correlated many-body systems, having two major properties: Strong spin-orbit interaction (shell effect) Collective motion (shape effect) Both effects are enhanced in heavier nuclei. Difference in excitation energy of the same spin between isobaric analogue states (IAS) of the same isospin T.
24 Isospin-symmetry breaking in excited nuclear states Isospin is to classify different nuclear states having same quantum numbers (e.g. same J and p). 51 Fe: N=25, Z=26,T z =-1/2 51 Mn: N=26, Z=25,T z =1/2 States of same T are clearly different. Warner, Bentley, Van Isacker, Nature Phys. 2 (2006) 311
25 More probes of isospin-symmetry breaking in nuclei Charge-symmetry breaking Experimental signal: Mirror energy difference (MED) -- difference between excited energies of T=1 isobaric analogue states (IAS) Charge-independence breaking Experimental signal: triplet energy difference (TED) ) INC is needed to interpret the MED and TED data in f 7/2 shell M. A. Bentley and S. M. Lenzi, Prog. Part. Nucl. Phys. 59 (2007) 497
26 INC effects for upper fp shell To account for the new A=66 TED data, INC nuclear force is needed. Kaneko, Sun, Mizusaki, Tazaki, Phys. Rev. C89 (2014) (R).
27 吸积盘
28 Isospin-symmetry breaking due to other structure effects M. Bentley Nucl. Phys. News, 22 (2012) 13. Two aligned neutron holes Two aligned proton holes
29 Isospin-symmetry breaking due to other structure effects M. Bentley Nucl. Phys. News, 22 (2012) 13.
30 Isoscalar neutron-proton pairing Possible evidence of T=0 n-p pairing: Cederwall et al. Nature 469 (2011) 68 Even if T=0 n-p pairing is not clearly presented in the ground state, it may show up at higher rotational frequencies. W. Satula, R. Wyss, Phys. Lett. B 393 (1997) 1. Completely different rotational behaviors between N=Z nuclei and N=Z+2 nuclei. Can it be an evidence for T=0 n-p pairing?
31 Isoscalar neutron-proton pairing Calculation by switching off T=0 n-p pairing gives nearly identical results for N=Z, N+Z+2, and N=Z+4 isotopes. This is because without T=0 pairing, which has the maximal effect for N=Z systems, two nucleons coupled to T=1, J=0 pairs can be easily destroyed by the Coriolis force. Preliminary results of shell model calculations by K. Kaneko.
32 Summary and questions Problem of isospin-symmetry breaking is interesting, and is a good selling point to other fields. Requirement of precise measurement of exotic masses has opened many possibilities for new facilities to contribute. One has begun to ask many questions regarding the nature of the symmetry breaking in nuclei with A>40. non-zero higher order T Z components in the IMME equation ground state with CDE and TDE excited spectrum with MED(J) and TED(J) in β decays between analog states Opportunities for the Rare-RI RIng in RIKEN!
33 Acknowledgement Theory: K. Kaneko (Fukuoka, Japan) T. Mizusaki (Tokyo, Japan) S. Tasaki (Fukuoka, Japan) Experiment: IMP, CIAE (China) GSI (Germany), York (UK)
34 CGS16 Shanghai, 2017 The 16 th International Symposium on Capture Gamma-Ray Spectroscopy and Related Topics Early September, 2017 Shanghai Jiaotong University, Shanghai, China
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