Anatoli AfanasjevMississippi State University, USA

GRETA/GRETINA: physical challenges – view of theorist

1. How do protons and neutrons interact to form nuclei?2. What are the origins of simple patterns in complex nuclei?3. What are the limits of angular momentum, excitation

energy, charge and mass for nuclei?4. What is the origin of elements?

Basic physics questions to GRETINA/GRETA

Single-particle degrees of freedom

GRETINA will have a factor of about 8 improvement in resolving powerrelative to GAMMASPHERE for lower multiplicity processes, such as Coulombexcitations and transfer reactions … … will greatly expand the opportunitiesfor advancing nuclear structure studies to higher spin, heavier mass, and to odd-A nuclei; all cases where the density of gamma-ray transitions exceeds the energy resolution achieved using present day gamma-ray detectors for in-beam spectroscopy

From GRETINA proposal

1. Single-particle properties of heaviest actinides better understanding of physics of superheavy nuclei

2. Single-particle properties of very neutron-rich nuclei better mass tables, better predictions for neutron-drip line, better understanding of

physics of neutron-rich nuclei

Experimental Experimental quasiparticlequasiparticlestates provide states provide

1. Important constraint for the 1. Important constraint for the selection of effective forces forselection of effective forces forthe description of the description of superheavysuperheavy

nucleinuclei2. Provide information about2. Provide information aboutspherical spherical subshellssubshells (high(high--j)j)

active in the vicinity of expectedactive in the vicinity of expectedshells gaps in spherical shells gaps in spherical superheavysuperheavy

A.V.Afanasjev et al, PRC 67 (2003) 024309

Analysis allowedAnalysis allowedto exclude the to exclude the NLSHNLSH andandNLRA1NLRA1 RMF forces fromRMF forces from

further applicationfurther applicationto to superheavysuperheavy nucleinuclei(the only sets which (the only sets which

predict Z=114 as shell gap)predict Z=114 as shell gap)

Quasiparticle spectra in heaviest actinide nuclei

corrected by the empirical shifts obtained in the detailed study of quasiparticlespectra in odd-mass nuclei of the deformed A~250 mass region (PRC 67 (2003) 024309)

SelfSelf--consistentconsistentsolutionsolution

RMF analysis of singleRMF analysis of single--particle energies in spherical Z=120, N=172 nucleusparticle energies in spherical Z=120, N=172 nucleus

RMFRMFdouble shell closure double shell closure

at Z=120,N=172at Z=120,N=172

SkyrmeSkyrme SkPSkP [m*/m=1][m*/m=1]double shell closuredouble shell closureat Z=126, N=184at Z=126, N=184

((SkMSkM*, *, ????????

SkyrmeSkyrme SkI3 [m*/m=0.57]SkI3 [m*/m=0.57]gaps at Z=120, N=184gaps at Z=120, N=184no double shell closure,no double shell closure,

SLy6SLy6

GognyGogny D1SD1SZ=120, N=172(?)Z=120, N=172(?)

Z=126, N=184Z=126, N=184

Low

eff

ectiv

e m

ass

Low

eff

ectiv

e m

ass

m*/

m ~

0.6

5m

*/m

~ 0

.65

Larg

e ef

fect

ive

Larg

e ef

fect

ive

mas

s m

*/m

~0.

8m

ass

m*/

m~

0.8 --

1.0

1.0

Which role effective mass plays???Which role effective mass plays???

Large density depressionLarge density depressionin the central part of nucleus:in the central part of nucleus:shell gaps at Z=120, shell gaps at Z=120,

N=172N=172

Flat density distributionFlat density distributionin the central part of nucleus:in the central part of nucleus:

Z=126 appears, Z=126 appears, N=184 becomes larger N=184 becomes larger

and Z=120and Z=120(N=172) shrinks(N=172) shrinks

Physics of neutron rich nuclei

S. Goriely, J.M.Pearson and Co

Skyrme functional: fit to masses allowedto decrease rms deviation (on masses) from~ 2.5 MeV down to ~ 0.7 MeV. In total ~20 parameters fitted to several thousands

of nuclei.Open questions: 1. No unique fit (how this affects the r-process abundancies???)

2. Should we use single-particleproperties as an additional

constraint on effective force?

Single-particle information has to be taken into account in orderto improve the quality of effective interactions (and probably, find missing channels of interactions) in the self-consistent theories.

Summary on single-particle properties

Example: extrapolability of mass tables to unknown nucleiFRDM (Moller, Nix) – good, rms error remains the sameSHF (S. Goriely, J.M.Pearson and Co) – deteriorates for older

parametrizations, unknown for newest ones From J.Rikowska-Stone, J.Phys. G: 31 (2005) R211

Principal difference between FRDM and SHF: careful fit of single-particledegrees of freedom.

There are > 80 Skyrme and > 40 RMF parametrizations, but they were fitted with no single-particle information taken into account.

Theory: careful fit of lowest single-particle states in deformednuclei within ‘a la table of mass’ strategy

Experiment: s-p states in heaviest deformed nuclei +s-p states in deformed neutron-rich nuclei

Jacobi transition

Rotational damping

Hyperdeformation

Order-chaostransition

FissionSpin limit

Spin

Normal-deformed(terminating)

Superdeformed(non-terminating)

Energy

(Near-)spherical

High-spin laboratory

# of p-h excitationsdeformation‘maximum’ spin

in the configuration

Rotating nuclei: the best laboratory for study of shape coexistence starting from spherical ground state

by means of subsequent particle-hole excitations one canbuild any shape (prolate and oblate [collective and

non-collective], triaxial, superdeformed, hyperdeformedetc.)

Termination and non-termination of rotationalbands

- basic feature of shell model- important feature of a finite many-fermion quantum mechanical system which either do not exist or cannot be experimentally measured in other quantum systems

Q1: Do all rotational bands end up in terminating states? How the transition from terminating to non-terminating bands takes place?

Q2. How the terminating states of smooth terminating bands are fed? (experimental proof of their termination)

Do all rotational bands end up in terminating states ???Do all rotational bands end up in terminating states ???T.Troudet and R. Arvieu, Ann. Phys. 134, 1 (1981)

Imax – the maximum spin which can be built in the pure configuration

Rotational bands do not terminatein a noncollective state at Imax if the deformation exceeds a critical

value at low spin.

Terminate Do not terminate

Cranked harmonic oscillator

Origin: due to the coupling of different N shells leading to a

mixing of different configurations

Even higher spins than Imax canbe build within the mixed

configuration.

Theoretical models:•CNS: Cranked Nilsson-Strutinsky

•CRMF: Cranked Relativistic Mean Field

No non-collective state can be defined for

I>Imax

Potential energy

surfaces for the GSB

configuration

Imax

Super- and hyperdeformation in neutron-rich nuclei.

- Mean field is well justified + pairing correlations are expectedto have negligible impact at high spin = clean probe of

effective interactions

Q1: How effective interactions are modified by neutron excessand fast rotation?

SD(2) is built on ph excitation acrossthe Z=48 SD shell gap. Crossing freq.

confirm its existence.

AA, S.Frauendorf, PRC 72 (2005) 031301(R)

J(2) of HD configurations = 67-71 MeV-1

N=60 and 62 SD shell gaps in CRMF.

SD(1)

SD(2)

-First hints for Hyperdeformation(“ridges” in γ−γ spectra)

compound nucleus at the highest spinsmost neutron-rich stable isotopes

48Ca + 82Se 126Xe + 4n

similar to the first observation of superdeformation ~20 years ago

Observation of hyperdeformed nucleiGamma-ray tracking arrayhigh intensity neutron-rich beams

Hyperdeformation

Superdeformation in nuclei around 68Zn

Hyperdeformation in the A~120-130 mass region

B. Herskind et al

Ridge structures in 3-D rotational mapped spectra are identifiedwith dynamic moments of inertia J(2) ranging from 71 to 111 MeV-1

Experiment:Wild variations of J(2): example 122Xe J(2)=77 MeV-1

124Xe J(2)=111 MeV-1

Preliminary CRMF: 122Xe J(2) (HD) ~ 75 MeV-1

Due to Z=30 and N=38 SD shell gaps

See M. Devlin et al, PRL 82 (1999) 5217

The presence or absenceof exotic nuclear shapes(swiss cheese, spaghetti

and lasagna phases) beforetransition to uniform npematter depends on the

assumed model of effective nucleon-nucleon interaction

‘SD’ and ‘HD’ in the crust of neutron stars

Rotating systems: the best laboratory

for time-odd mean fields

Time-odd mean fieldsOpen questions:dependence on deformation,configuration, spin, isospin etc. ????Method: to eliminate the uncertainties related to pairing use high-spin data

Impact of time-odd meanfields (in %)

Wobbling motion

Q1: Can wobbling excitations be observed in other regionsof nuclear chart in which theoretical calculations strongly

suggests the existence of triaxial shapes at high spin?

Q2: What are the basic conditions for the existence of wobbling excitations?

- unique signal of triaxiality of nuclei

110110Sb Sb yrastyrast band configuration band configuration [21,3] = [#[21,3] = [# gg9/29/2

--11 ## hh11/211/2, #, # hh11/211/2]]

see A.V.Afanasjev, D.B.Fossan, G.J. Lane and I.Ragnarsson, Physics Report 322 (1999) 1

Theoretical calculations suggests that many rotational bands possess appreciable triaxiality over considerable spin range:

1. Smooth terminating bands in the A~110 and A~60 mass regions

2. Many normal- and highly deformed rotational bands in the A~60-80 and A~130 mass regions

3. Superdeformed bands in the A~80 mass region

D.G.Sarantites et al,PRC 57 (1998) R1

Wobbling motion

Wobbling excitations were not observed in these regionsof nuclear chart so far !!!

Possible reasons:1. Do not exist in these nuclei. Why?

2. Wobbling excitations in are highly non-yrast in these nuclei??? Will GRETA be able to measure such

excitations?

Giant Resonances

The GDR position has been measured for about 90 stable nucleiall lying on beta stability line.Extend these measurement to 1. Unstable neutron- and proton-rich nuclei2. To high spin systems