Nuclear structure in the weak process

JUNO-Neutrino, IHEP, July 11, 2015

Yang Sun (孙扬 )Center for Nuclear Astrophysics (CNA)

Shanghai Jiao Tong University (SJTU), China

Neutrino in Wikipedia

Neutrino was postulated first by Wolfgang Pauli in 1930 to explain how beta decay could conserve energy, momentum, and angular momentum (spin).

Neutrinos can interact with a nucleus, changing it to another nucleus.

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a proton is transformed into a neutron, or vice versa, inside an atomic nucleus. This process allows the atom to move closer to the optimal ratio of protons and neutrons.

The periodic table

Neutron star

超新星爆发

X-射线爆

中子星merger

Production of heavy elements

已知 118种核素 ( 包括近年来新发现的、还未命名的 )

只有不到 300个稳定的同位素 ( 对此我们有一定认识 )

对大部份非稳定同位素有所知 , 但知之不多

对其余几千个远离稳定区的同位素性质则一无所知

The family of isotopes

s process

p process

Pb (82)

Sn (50)

Fe (26)

H (1)protons

neutrons

stellar burning

Big Bang

Cosm ic Rays

Supernovae

rp process

r process

M ass know nH alf-life know nnoth ing know n

How are the isotopes synthesized?

Neutron star

rp-process =Rapid proton capture process

One of the major processesfor heavy element production

Most of the time is spent at the waiting point nuclei

rp-process in x-ray burst

27282930 3132 333435 3637383940 4142 4344

45 464748

495051 52

535455

56

5758

5960

61 62 6364 656667 68697071 727374

75 76 7778

7980 8182

G a (31)G e (32)As (33)

Se (34)Br (35)Kr (36)Rb (37)

Sr (38) Y (39)

Zr (40)Nb (41)

M o (42)Tc (43)

Ru (44)Rh (45)Pd (46)Ag (47)

Cd (48)In (49)

Sn (50)Sb (51)

Te (52) I (53)

Xe (54)

0 20 40 60 80 100 12010

-6

10-5

10-4

10-3

10-2

68

72

76

abun

danc

e

64

104

80

Mass number

slow decay (waiting point)

Waiting point nuclei

Important role of nuclear structure in nucleosynthesis

Nuclear structure controls the clock for the stellar processes the total time along the reaction path entirely determines the

speed of nucleosynthesis towards heavier nuclei and the produced isotopic abundances

We need to know: nuclear masses (ground state properties, energy gaps, single-

particle levels, ...) nuclear structure (nuclear deformation, collective excitations,

quasiparticle excitations, isomeric states, …) capture rates -decay rates

The astrophysical processes of nucleosynthesis involve those nuclei, which are unstable isotopes. We do not know much about their properties.

These nuclei are very short-lived, close to the drip line, and therefore, are very challenging experimentally.

Some of their properties can be experimentally measured, but require new concepts in facilities.

Some of them can not be measured, even not in principle.

Request of advanced facilities

Stellar enhancement of decay rate

A stellar enhancement can result from the thermal population of excited states

Examples in the s-process

m mm

iii

i jiji

kTEI

kTEIp

p

/exp12

/exp12

F. Kaeppeler, Prog. Part. Nucl. Phys. 43 (1999) 419

Double decay is a very rare transition between two nuclei with the same mass number (A) that changes the nuclear charge (Z) by two units Typically, decay from the ground state (spin and parity 0+) of an

initial even-even nucleus to the ground state (also 0+) of an final even-even nucleus

Two-neutrino decay, (2)

conserves lepton number

Neutrinoless decay, (0)

violates lepton number – thus forbidden in the Standard Model

Double beta decay

Majorana particles are identical with their own antiparticles

Detection of the neutrinoless double decay would imply evidence of physics beyond the Standard Model and the neutrino is a massive Majorana particle

If (0) decay is by the exchange of a massive Majorana neutrino, the half-life is

Phase-space integral

Nuclear matrix elements

Neutrino mass

Majorana neutrino

Advanced Facilities: Storage rings

HIRFL-CSR at Lanzhou, China

ESR at GSI, Germany

Tz=-1

/2, (

78 Kr B

eam

)

Tz= -1

, -3/

2, (

58 Ni Bea

m)

Experiment in Lanzhou

A tiny value changes in nuclear structure can cause big changes in astrophysical 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

Study of isospin-symmetry breaking and n-p pairing could impact nuclear astrophysics

Tiny changes in nuclear structure could make it `big’ in astrophysics

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 63Ge, 67Se.

It shows some differences for 65As and 71Kr.

Mass measurement results in Lanzhou

89%–90% of the reaction flow passes through 64Ge via proton capture indicating that: 64Ge is not a significant rp-process waiting point.

1

Abundance of x-ray burst ashes

Stellar weak interaction rates

Study of stellar weak interaction rates in astrophysics is essentially a nuclear structure problem Pioneering work of G. Fuller, W. A. Fowler, M. J. Newman

Decay rates are determined by the microscopic content of nuclear many-body wavefunctions

Nuclear shell model (diagonalization of an effective Hamiltonian in a chosen model space) is the most preferable method for GT transition calculations. M. B. Aufderheide, S. D. Bloom, D. A. Resler, G. J. Mathews,

Phys. Rev. C 47, 2961 (1993). K. Langanke and G. Martınez-Pinedo, Rev. Mod. Phys. 75,

819 (2003).

Nuclear structure models

Description of the strongly correlated many-body systems – two popular methods:

Shell-model diagonalization method Based on quantum mechanical principles Growing computer power helps extending applications A single configuration contains no physics Huge basis dimension required, severe limit in applications

Mean-field approximations Applicable to any size of systems Fruitful physics around minima of energy surfaces No configuration mixing, results depending on quality of mean-field States with broken symmetry, usually cannot study transitions and

decay rates

Beyond the mean fields

Quasiparticle Random Phase Approximation (QRPA) is the current method for heavy nuclei, particularly for forbidden transitions Build 1p-1h correlations on top of a mean field D. Rowe, Rev. Mod. Phys. 40, 153 (1968)

Not a shell model, may contain spurious components in wavefunctions

For deformed nuclei, calculated nuclear states are usually not angular momentum states, but K-states (which are mixtures of I-states)

Development of nuclear structure theories

The group at shanghai Jiao Tong University has worked actively on the development of new shell models.

It has established the unique model using the projection method and the Pfaffian algorithm for numerical computation.

How to treat heavy, deformed nuclei

Most nuclei in the nuclear chart are deformed. To describe a deformed nucleus, a spherical shell model loses advantages.

One can start from a deformed basis by breaking the rotational symmetry spontaneously.

Then apply angular-momentum-projection technique to recover the symmetry. important correlations prepared through a good mean-field intrinsic states classified with well-defined physical meanings these states transformed to the laboratory frame diagonalization performed in the (angular-momentum)

projected basis

Novel method connecting mean-field and shell models

Angular-momentum projection method based on deformed mean-field solutions Start from intrinsic bases (e.g. solutions of deformed mean-

field) and select most relevant configurations Use angular momentum projection technique to transform

them to laboratory basis (many-body technique) Diagonalize Hamiltonian in the projected basis (configuration

mixing, a shell-model concept) It is an efficient way, and probably the only way to treat

heavy, deformed nuclei with a shell model concept

The Projected Shell Model (PSM):• K. Hara, Y. Sun, Int. J. Mod. Phys. E 4 (1995) 637

Multi-quasiparticle computation using the Pfaffian algorithm

Calculation of projected matrix elements usually uses the generalized Wick theorem

A matrix element having n (n’) qp creation or annihilation operators respectively on the left- (right-) sides of the rotation operator contains (n + n − 1)!! terms in the expression – a problem of combinatorial complexity

Use of the Pfaffian algorithm: L.M. Robledo, Phys. Rev. C 79 (2009) 021302(R). G. Bertsch, L.M. Robledo, Phys. Rev. Lett. 108 (2012) 042505. T. Mizusaki, M. Oi, Phys. Lett. B 715 (2012) 219. M. Oi, T. Mizusaki, Phys. Lett. B 707 (2012) 305. T. Mizusaki, M. Oi, F.-Q. Chen, Y. Sun, Phys. Lett. B 725 (2013) 175 Q.-L. Hu, Z.-C. Gao, Y. S. Chen, Phys. Lett. B 734 (2014) 162.

L.-J. Wang et al. Phys. Rev. C90 (2014) 011303(R)

A third band-crossing is described.

Extension of configuration space to 6-qps.

Associated institution of JINA-CEE Promote nuclear astrophysics development in China Promote international collaborations and academic

exchanges in this field Carry out conversations from different fields in China

Nuclear experimental facilities in IMP (Lanzhou), CIAE (Beijing) JinPing underground lab (Sichuan) JiangMen neutrino lab (Guangdong) Shanghai synchrotron light (upgrade to provide gamma rays) Strong laser facilities (ShenGuang) Large telescope LAMOST (Beijing) Supercomputer Tian-He (Tianjin)

Nuclear astrophysics center at Shanghai Jiao Tong University

Center for nuclear astrophysics (CNA)

Summary

The discovery of neutrinos was made in nuclear physics through beta decay.

In nuclear physics, weak processes occur in parent nuclei, and therefore, the knowledge of nuclear many-body systems is involved.

Some quantities can be measured experimentally, but many others have to rely on theoretical calculations.

It defines a close relation between neutrino physics and nuclear physics.