testing isospin -symmetry breaking and mapping the proton drip-line with lanzhou facilities
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Testing isospin -symmetry breaking and mapping the proton drip-line with Lanzhou facilities. Yang Sun Shanghai Jiao Tong University, China. SIAP, Jan.10, 2013. The concept of isospin. Formalism first applied to nuclei by Heisenberg W. Heisenberg, Z. Phys. 77 (1932) 1 - PowerPoint PPT PresentationTRANSCRIPT
Testing isospin-symmetry breaking and mapping the proton drip-line
with Lanzhou facilities
Yang SunShanghai Jiao Tong University, China
SIAP, Jan.10, 2013
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
1/ 2t 1/ 2zt 1/ 2zt
1( ) ( ) / 2
A
z ziT t i N Z
, 1, , 1,zT T T T T
Isospin is only an approximate symmetry
Phys. Rev. 51 (1937) 106
Classify different nuclear states having same quantum numbers
51Fe: N=25, Z=26,Tz=-1/251Mn: N=26, Z=25,Tz=1/2
Isospin symmetry
Warner et al., Nature Phys. 2 (2006) 311
Suppose attractive nucleon-nucleon interaction is v Charge symmetry: vnn = vpp
Charge independence: vnp = (vnn + vpp) / 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
This can be easily derived:
Let HCI be charge-independent Hamiltonian, is its
eigenstate. H’CV is charge-violating interaction
Assuming two-body interactions:
Isospin-symmetry breaking
Taking H’CV as perturbation
One obtains the famous Isobaric Multiplet Mass Equation (IMME):
which depends on Tz up to the quadratic term.
Isospin-symmetry breaking
Higher orders of Tz (dTz3, eTz
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
Isospin-symmetry breaking
IMME has beentested up to A~40
Tz=-1
/2, (
78 Kr B
eam
)
Tz= -1
, -3/
2, (
58 Ni Bea
m)
Experiment in Lanzhou
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
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 forA=53, T=3/2 quartet.
A non-zero d term isneeded.
Y.-H. Zhang et alPRL (2012)
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)
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
2 ( ) ( ) ( 2)D A D A D A
?
Odd-even staggering explained by E. Feenberg and G. Goertzel, Phys. Rev. 70 (1946) 597
?
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
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
吸积盘
The charge-dependent and isospin nonconserving forces are considered:
V’CV
VC: 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
Comparison of calculated difference in CDE with GXPF1A and JUN45 forces with A. Brown calculation and measurement .
Theory or exp problem?
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 and2-proton separation energy
For even-mass nuclei,T=1,2,3
The first PRL of X. Tu et al., through the 65As mass concluded that 64Ge is not a good waiting-point nucleus.
Precise mass measurement for 69Br which can determine the waiting-point property for 68Se. Precise mass measurement for 73Rb which can determine the waiting-point property for 72Kr. 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?
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