Doctoral Defense of Barak Hadina18th January 2008

In-Beam Study of Extremely Neutron Deficient Nuclei Using the Recoil Decay Tagging Technique

Opponent: Dr. Paddy Regan, Department of PhysicsUniversity of Surrey

Guildford, UK

What are the ‘Big Questions’ in Nuclear Physics?

1. What are the limits of nuclear existence ? What combinations of protons and neutron can exist ?

2. How do nuclear properties change at extremes of proton and neutron separation energy; how is the single-particle structure altered under ‘extreme’ conditions including rotational stress ?

3. Are there any new collective effects or symmetries apparent in extreme nuclei, such as extra proton-neutron pairing at N ≈ Z ?

4. What effect do nuclear structural properties have on explosive nucleosynthesis (such as the rapid-proton capture process)?

What are the limits of nuclear existence ?• Nuclear chart is ‘bounded’ by the proton and neutron drip-lines S n ,Sp <0. • Particle ‘drip lines’ are defined by ground-state, particle radioactivity.

• Some cases, -decay also puts a limit on what is ‘bound’.

Nuclear mass formulas(vital inputs for nuclearastrophysics calculations) are excellent at explaining‘known’ masses….

BUT…..

at the extremes of N : Z(e.g., 106Te, 110Xe) which one is correct ?Need data to constrain these models……

decay can determine masses to high accuracy (if the parent mass is known).

Mass differences for Sn (Z=50) isotopes

Nuclear Excited States – Nuclear Microscopy…

Nuclei can exist in either the ground state or an excited stateDecays from excited states tell us about the internal structure!!!Each nucleus is different….but groups of structural patterns do appear….

Evidence for Nuclear Shell Structure?

Nuclei with magic numbers

of neutrons/protons have:N=50 N=82 N=126

21+ state at higher energy

Low values of B(E2: 21+→0+)

(i.e. small transition probability)N=126

N=82

N=50

E(2+) and B(E2) apparently correlated….small E(2+) usuallyhas large B(E2) and vice versa.

Signatures of Nuclear Structure ?

• E(2+) value related to B(E2) by Raman’s empirical relation.

• E(4+) / E(2+) = R4/2 is a measure of collective effects in nuclei.

– Rotor = nuclear quadrupole deformation has Ex(I) ~ I(I+1), • R4/2= (4x5)/(2x3) = 20/6 = 3.33

– Perfect (harmonic, spherical) quadrupole vibrator has, Ex(I) ~ I,• R4/2= 4/2 = 2.00

– Axially asymmetric rotor, gamma-soft nucleus, R~2.5

Fusion-Evaporation Reactions

• Typical geometrical cross-section in fusion is given by ~b2, where b~1.2(A1+A2)1/3 fm.

i.e., expect tot~30 fm2 = 0.3 barns (1b=10-28m2)

KEbeam > ECoulomb to form compound nucleus.Ebeam & Q-value lead to excitation energy, lost by particle evaporation.

Reaction used in thesis to create 106Te was 54Fe+54Fe →108Te*,

Main evaporation channels from 108Te* are 3p →105In, 2pn →105Sn, 2p →106Sn, a2p →102Cd, etc. since Sp < Sn.

Most exotic final channel is 2n →106Te, ~25nb.

Problem ? How do you select events with 25nb out of 0.3b ? i.e., need channel selection to accuracy of ~1 part in 107?

b

Spectroscopy ‘beyond’ the drip-line ?

• Coulomb barrier → unbound protons and/or s are hindered in their decay, i.e., unbound nuclei have finite lifetimes.

• If gamma-ray decays of excited states are short (fs → ns) compared to ground state decay, these can decay before.

• The discrete ground state decay can be used as a ‘tag’ for the gamma-rays as coming from the specific nucleus of interest → Recoil Decay Tagging Technique

T1/2 (108Te)= 2s; E=3.3 MeV(2p2n chan)

Nuclear Alpha Decay

Conservation of energy

mXc2 = mX’c2 +TX’ +mc2 +T

Q-value for the decay

Q = (mX - mX’ - m ) × c2

= TX’ + T

Conservation of momentum p = pX’

so p2 / 2m >> pX’

2 / 2mX’ T >> TX’ typically 5.0 MeV : 0.1 MeV

The Coulomb potential 1/r outside nucleusThe nuclear potential << 0 inside nucleus

Q-valuetypically5 → 6 MeV

b Is ~40fm (determinedby decay Q-value).a is typically

~8 fm.

For A~200, barrier height , B at a is typically 34 MeV

The -particle inside can tunnel to the outside, the wave function decays exponentially through barrier

~ ×10 - 4 per MeV

Geiger-Nuttall rule

log t 1/2 = (const / Q) - const

Height of the Coulomb barrier

C =

Radius where barrier is cleared

b =

k 2 = ( 2m/ 2 ) × ( V (r) - Q ) a

× e - k r through the barrier

Probability to penetrate barrier P = e - 2 G

where the Gamow factor G is

G = ( 2m/ 2)1/2 a

b

( V(r)- Q) 1/2 dr

P is bigger (G smaller) for larger QGeiger-Nuttall rule follows

Nuclear Alpha Decay

1 z Z’ e2

40 a

1 z Z’ e2

40 Q

Angular momentum adds an additional centrifugal potentialVcentrifugal = (+1) 2 / 2m r 2

adding an dependent additional barrier

Decays favour large Q and small value

0+

4+

6+

2+

0+

0.0046 %

0.035 %

25.0 %

74.0 %

24296Cm

23894Pu Q g.s. = 6.216 MeV

t 1/2= 163 d

= ( -1 )

aside:

Physics at N≈Z, np Pairing• Protons and neutrons in same orbitals, extra coupling

might mean extra collectivity. • Most likely at N≈Z (due to large spatial overlap of orbitals).

• Problem? Formation of heavy N~Z nuclei hard with fusion-evaporation reactions (106Te, Sn~10.5 MeV, Sp~1.3 MeV).

nn ppnp

T=1, S=0

T=0, S=1

TZ: +1 0 -1

First data on 106Te, E(2+) significantly lower in than expected from shell model calculations.

What is missing, evidence for np pairing ?

Note, experimental ‘tour de force’ at =25nb !!! 106Te

110Xe (Z=54, N=56) has Tz=+1.Most exotic Xe isotope studied to date.

One expects E(2+) to increase and R4/2 to decrease compared to 112Xe...

BUT the opposite happens!

Is this evidence for new collective effects which only are apparent at N≈Z(i.e., np pairing ) ?

(a) use 2-step decay to select 110Xe events. (b) RDT gives 1st 110Xe decay scheme.

110Xe

Xe (Z=54) isotopes

RDT also applicable to heavier, alpha/protondrip-line systems.

Fine structure (i.e., l-dependence in decay) shows up dramatically in odd-odd systems (such as 170Ir and 166Re).

More complicated spectrum than A~110 region.

Fine structure allows RDT to be used on specific single-particle coupling configurations.

Tagging gives level scheme.Structural assignment based on

(a) Fine structure of alpha-decay(b) B(M1)/B(E2) branching ratios(c) Alignment properties

Summary of new physics present in thesis• First experimental investigation of excited states in VERY neutron

deficient nuclei 106,7Te and 110Xe.

– Energy of (7/2+) state in 107Te important for the rp-process.

– 106Te new in-beam ‘world record’ at 25 nb cross-section. Possible evidence for np-pairing ?

– 110Xe, increased collectivity compared to 112Xe. Evidence for np-pairing ?

• Evidence for rotational bands and significant