Su Shi Chun

• From experiments, we found that nuclei are more tightly bounded

number of protons or neutrons is 2, 8, 20, 28, 50,

82, 126 (Magic numbers).

• Analogous to electron configuration

valence nucleons in a nucleus are moving in an average(mean field) potential of the core (closed shell).

nuclear shell structure is different from electron shells, e.g. with strong nuclear force

• Each valence nucleon has corresponding n, l and j values like electrons.

1s1/2

1p1/21p3/2

1d5/2

• Simplest shell model independent particle model nucleons do not interact with

core or with each other limited applications but get the Nobel prize for Meyers and

Jensen.

• Realistic shell models which are useful to compare to data must include residual interactions between nucleons and

core two-body and three-body force that are very difficult to include theoretically

• To calculate SF, we use Oxbash by Alex Brown (MSU)

• Spectroscopic factor describes the configuration of the valence (transfer) nucleon orbitals corresponding to the shell model.

• Spectroscopic factors can be calculated by shell model. (Theoretical approach)

• To measure spectroscopic factors, one needs a reaction model. (Experimental approach)

• SF is a fundamental quantity in shell model and can be used to test other assumptions used in shell model including selection of the interactions used in shell models.

• Not elastic collision.

• The neutron from the deuteron is transferred to the target nucleus.

• Unlike collision in classical physics Deal with wave functions. (not particles)

• No exact wave

functions can be

found.

• Approximation is

needed---ADWA.

• Spectroscopic factors (SF) determine the reaction rates of rp capture

important for analyzing evolution of neutron stars.

• The rp process (rapid proton capture process)

consecutive proton captures onto seed nuclei to produce heavier elements.

It is responsible for the generation

of the heavy elements in the universe.

Most SFs of the relevant states (excited states) are not available experimentally calculated by shell model.

Therefore, it is important to establish the accuracies of these calculations by com

paring experimental spectroscopic factors.

Use MIRROR NUCLEI!!

•Assume the coulomb repulsion is small compared with other interactions insides the nuclei!

•Proton capture neutron capture/stripping

K35 S35

Very little is known about the states in 35K which lies on the rp process path.

There are much more information on 35S (mirror of 35K) which is close to the valley of stability.

Si31

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

SF_Excitation Energies

SF

_E

x f

rom

Jo

urn

als

Betigeri

line

Watson

Piskor

Wildenthal

ddExd

dTh

Oxbash for Theoretical ModelTWOFNR for Experimental SF

SF_Ex=

Johnson- Soper Adiabatic Approximation to take care of d-break-up effects – Adiabatic 3-bodies model

Use global optical potential with standardized parameters (CH89)

n-potential : Woods-Saxon shape r0 =1.25 fm & a0 =0.65

For ground state only, SF>0.2

What happen to small SF<0.2 ?

Results from Jenny Lee --2004 SURE student"

Open for USD, solid for USDA

0.0001

0.001

0.01

0.1

1

0.0001 0.001 0.01 0.1 1

SF_Oxbash

SF_E

xper

imen

t

Mg27 Cl36

Si31 S35

line 0.8line

1.2line Mg27

Cl36 Si31

S35

Open for USD, solid for USDB

0.0001

0.001

0.01

0.1

1

0.0001 0.001 0.01 0.1 1

SF_Oxbash

SF_E

xper

imen

t

Mg27 Cl36

Si31 S35

line 0.8line

1.2line Mg27

Cl36 Si31

S35

USDB

0.0001

0.001

0.01

0.1

1

0.0001 0.001 0.01 0.1 1SF_Oxbash

SF_E

xper

imen

t

Mg27Cl36Si31S35Ca43line0.8line1.2line

Excited states extent to much smaller SFs !!

• By using a consistent analysis approach, we are able to extract spectroscopic factors of the excited states from different reactions and compare between them

• Application of the method to excited states allows comparison of small SF values with theory

• The extracted spectroscopic factors are sensitive to different interactions used in shell model calculations

• With the newest interaction USDB, the comparisons between experimental and theoretical values is good to within 20% uncertainty for SF as small as ~0.001 – the theoretical uncertainties are important in astrophysics network calculations

Special thanks : Prof. Chu at CUHK Prof. Tsang at MSU Jenny Lee at MSU