MoN

MoNA Talk July 20

Kirby Kemper

Florida State University

Nuclear reactions change a given set of nuclei into other nuclei. With them we can achieve the

long sought transformation of elements

As far as we know the first observation of a nuclear reaction was when Rutherford’s students observed very long range “alpha”particles coming from the

radioactive sources that they were using for their elastic scattering measurements.

The reaction they were observing was 14N(α,p)17O

Nuclear Reactions- Many Names:

Compound Nucleus

Direct

Fusion

Fission

Deep Inelastic Scattering

Resonances

Simplest process and most probable of happeningis elastic scattering. Here projectile scatters from

target and comes in in its ground state and is detectedin its ground state.

You can also have inelastic scattering where no massis transferred between the target and projectile but only

energy.

Some notation notes:

Normal Kinematics: target( beam, outgoing) residual nucleus

14N(α,p)17O “beam” particles are lighter than the target nuclei

Inverse kinematics: 4He(14N,17O)p heavy beam strikes lighter target

For a lot of radioactive beam work we are working in inverse kinematicswhere we might have a 48Ca beam striking a 9Be target and knock

six protons and four neutrons from the beam to make 38Siand then the 38Si strikes another 9Be target where two

protons are knocked out to make 36Mg, the nucleus of interest9Be(48Ca,38Si)23Ne 9Be(38Si,36Mg)11C

Start with 50pnA of 48Ca make 4000 38Si per second or 3x1011 48Ca particle/sec to make 4000 38Si/sec

to then make 15 36Mg per hour

Direct Reaction- Takes place quickly~ 10-22 sec

time it takes for a nucleon to cover the width of a nucleus

single step that links the initial nuclear state

with the final one

Compound Reaction- multi-step processwhere the compound nucleus forgets

how it was formed

formation and decay are independent

overlap of initial and final states does not enter into analysis

There are two ways in which physics tries to obtain a consistent picture of the structure of the atomic nucleus. One of these is the study of the elementary particles, their properties and mutual interactions. Thus one hopes to obtain a fundamental knowledge of the nuclear forces, from which one can then deductively understand the complicated nuclear structures. The other way consists in gaining, by direct experimentation, as many different data as possible for individual nuclei, and examining the relations among these data. One expects to obtain a network of correlations and connections which indicate some elementary laws of nuclear structure. These two ways have not yet met to establish a complete understanding of the nucleus, although many connections have been found.

From Introduction to“Elementary Theory of Nuclear Shell Structure” M.G. Mayer and J.H.D. Jensen 1955 p vii

So, our job is to learn about nuclear structure and or reaction models with any tool at our disposal

Reactions where we detect the charged particlesgammas and neutrons produced

Beta decay with neutrons, charged particlesand gammas

Magnetic moments

What has made it possible to study nuclei like 36Mg are greatly more efficient detection systems

MoNA is one such system where a system had to be built that would handle the much higher neutron energies that occurred with the use of the coupled cyclotrons that

would let us make nuclei much closer to the neutrondripline

The new complicated systems require collaborationsof many individuals to make them work

Lets pick on example of study: structure of nuclei at the neutron dripline

Just as need new ion source and detectorsystems for the study of these exotic nuclei

we need new theoretical techniques tohandle the calculation of nuclear structureand reactions of nuclei that are either just

bound or in fact are unbound

Consider elastic scattering- a well understoodprocess for heavy-ions

Huge change in computing capability allows for bothnew experimental systems by integrating the computerinto the detection system and new theory capabilities.

In 1976 on calculation took 50,000 cpu seconds and cost $1000

Today same calculation takes 3 seconds on my laptop and costs??? .00001 cents

Not speed of computer but cheap memory

However, we are now learning what physics we don’t understand becausewe can put in physics effects that

weren’t possible before

Classic Fresnel scattering problem

Take a few examples of how we develop nuclear structureKnowledge

Coulomb Excitation (tells us about the proton properties)Extract B(C2)

to learn about the mass properties do inelastic proton scattering extract B(E2)

Mass (particle) transfer reactions

In-beam spectroscopy with fast beams at rates of a few nuclei per second

• NR × NT × NB

Cross section– NT Atoms in target– NB Beam rate– NR Reaction rate

• Example

= 100 mbarn

– NT = 1021 cm-2

– NB = 3 Hz

– NR =26/day = 3×10-4 Hz

• Fast exotic beams allow for

– thick secondary targets (100-1000 thicker than at low energy)

– event-by-event identification

– Clean trigger

beam targetscatteredbeam

Luminosity gain of 100-1000 …… measure recoils and use photons to indicate inelastic scattering

Intermediate-energy Coulomb excitationReduced transition matrix elements independent of impact

parameter

Experiment:

Max. determines min. b

A. Gade et al., Phys. Rev. C 68 (2003) 014302.

adopted

Our definition of a direct reaction

selective population of the same states in the final nucleusat several bombarding energies that are different by

no more than a factor of 2 or so by the same reaction ((d,p) at 7.5 MeV/amu and 15 MeV/amu)

selective population of the same states in the final nucleusby different reactions that transfer the same particle (say

one proton or one neutron)(d,p) (7Li,6Li) (13C,12C)

Here we haveselective populationbut states populatedchange rapidly asbeam energy changes.

Not Direct Reaction

Why do we repeat reactions that seem to give the same information?

For example, (d,n)

(3He,d)(α,t)

(7Li,6He)(16O,15N)

we can populate levels with differentintensities by using angular momentum mismatch,

and the fact that the transferred proton comesfrom different orbits in the projectile

(α,t) will favor high spin orbits compared with (d,n)

use every trick we know to get info

So now you have measured a cross section (the probability for a transition to occur

What does it tell us about the nucleus?

Here we need theory

For mass transfer first try what is known as the distortedwave theory or DWBA –used a low energies (10 MeV/amu)

From this theory you can learn the spin of the nuclearstates you are populating and also theory

probability of looking like the target+particle

Distorted Wave Born Approximation (DWBA)

A simple one step stripping reaction may be written diagramatically as

A + a → B + b

A + (b + x)a → (A + x )b + b

where A represents the target core, b represents the projectile core, and x is the

transferred mass which may represent any number of particles.

DWBA Formalism (d,p)

State InitialˆState Final TotalVT pnpndAppApnBp rdrdrrAUVVAT

),,()1( )( pndApnBp rdrdrVAT 0)()1(

Initial StateInteraction

Final State

pnddAppApnBp rdrdUVVAT 0)1(

Assumptions of DWBA

• Single Step transfer of nucleon to target-core.– 1st Born Approx., 1-step process, Direct– Core is not excited in process– Projectile remains in ground state

• Distorted Waves derived from elastic scattering– Assumes wave does not change much during

scattering

• Transfer reactions are weak compared to elastic scattering.

• This formulation is spin-independent.

Spectroscopic Factor

BJnnljAA nlj

nljB rABAA )]()()[,'()1( ''

Parentage: Sum over all possible configurations of targetand nucleon states that produce final state. Only one of these (A’=A) is the pure single-particle state in DWBA.

Amplitude of each state

),(or 22 BASCS nlj

DWBAerimental d

dSC

d

d 2

exp

S.F. is probability that state B is produced in reaction.This is the quantity that is compared to structure theory

Single Particle Transfer at Intermediate Energies (3)

• Radioactive beam experiments are often conducted at intermediate energies and in inverse kinematics.

• Forward focused beam and reaction products; difficult to get elastic scattering measurement on composite target (like “d”).

Eikonal Model [6]

• Knockout Reactions create many-body final states with: – removal (stripping) of the nucleon by deuteron breakup – elastic breakup (diffraction dissociation) of the projectile

[6] P.G. Hansen and J.A. Tostevin, Annu. Rev. Nucl. Part. Sci. 53 (2003) 219

Background Single particle states are strong if particle is Single particle states are strong if particle is

transferred to nucleus. transferred to nucleus. Single hole states are strong if particle is removed Single hole states are strong if particle is removed

from nucleus. from nucleus.

4848Ca(Ca(77Li,Li,66He)He)4949ScScK.W. Kemper et al. Nucl. Phys. A348, 339 (1980)K.W. Kemper et al. Nucl. Phys. A348, 339 (1980)

5.09 MeV

4.49 MeV3.08 MeV

G.S.

5050Ti(d,Ti(d,33He)He)4949ScScP. Doll et al. J. Phys. G, Vol. 5, No. 10, 1421 (1979).P. Doll et al. J. Phys. G, Vol. 5, No. 10, 1421 (1979).

2.23 MeV

2.36 MeV

4.01 MeV

One-neutron knockout on N=16 nuclei

.

.

• Primary beam 36Ar (150 MeV/nucleon)

• Primary target: 9Be (1034 mg/cm2)• Knockout target: 9Be (188 mg/cm2)• 34Ar @ 70 MeV/nucleon (mid-target)

33Cl @ 66 MeV/nucleon 32S @ 63 MeV/nucleon• Particle ID with S800• Momentum reconstruction with S800• γ-ray spectroscopy with SeGA

…

primary beam

31Ar 32Ar 33Ar 34Ar

35K

33Cl32Cl31Cl

one-neutron knockout N=16N=15

31S29S 32S 33S30S

35Ar

34Cl 35Cl

34S

36Ar

N=15

• more than 50MeV/nucleon: sudden approximation + eikonal approach• Spectroscopic Factors determined from the population of the residue with A-1

Spectroscopy of the wave function:

One-nucleon knockout

),(),()( 2

jnsp BjInjSCnI

diffrstrip ),(),(),( nspnspnsp BjBjBj

P.G. Hansen and B.M. Sherrill, Nucl. Phys. A 693, 133 (2001).P.G. Hansen and J. A. Tostevin, Annu. Phys. Rev. Nucl. Part. Sci., in press

nuclear structureinformation

reaction process

residue moment distribution -value of knocked-out n

Inclusive momentum distributions

.

.

11.6

100

11.0

11.4

11.2

200

0

Cou

nts

/ 16.

7MeV

/c

P || (GeV/c)

knockout residues

Fragment momentum distribution (longitudinal):depends on angular momentum (-value) of the knocked-out neutron

Inclusive momentum distribution: contains all particles superposition of excited-state and ground-statemomentum distribution

-value assigned in comparison to model calculations(black-disk approximation)

=0 =2

P.G. Hansen, PRL 77, 1016 (1996)

Momentum distributions for the knockout to individual final states

.

N=8

d5/2

s1/2

excited final state of 33Ar

ground state of 33Ar

= 2

= 0C

ount

s / 3

6.2M

eV

0

50

100

150

200

100

300

200

0

11.2 11.411.6 11.211.4 11.6

P || (GeV/c) P || (GeV/c)

= 0 = 2

in coincidence with γ-rays

knockout residueswithout γ-ray

A. Gade et al., PRC 69 034311(2004)

34Ar

γ-ray spectroscopy to tag the final state

Sp=3340(30) keV

1358(5) keV

1795(7) keV

0.0 keV

3818(11) keV

(5/2+)

3/2+

5/2+

1/2+

4047.8 keV

1847.6 keV

1431.6 keV

3/2+

5/2+

5/2+

(level scheme confirmed by PhD thesis of R.R.C. Clement, MSU 2003)

1000 1500 2000 2500 3000 3500

50

0

100

Cou

nts

/ 13

keV 2460(9) keV

1795(7) keV

1358(6) keV projectile frame v/c=0.363

33Ar

Energy (keV)

BR (%) exp (mb) C2Sexp

1/2+ 30.2(46) 4.7(9) 0.38(6)

3/2+ 20.2(44) 3.2(8) 0.36(9)

5/2+ 31.7(31) 4.9(7) 0.56(8)

(5/2+) 17.9(30) 2.8(6) >0.34(7)A. Gade et al., PRC 69 034311 (2004)

Adiabatic Model Calcs. [2]

[4] J.A. Tostevin, M. Igarashi, et al. – Computer Program “TWOFNR”

Cross Section Comparison Between Theory and Experiment

State (MeV) L-value [3] Sigma [4] C2S [3] Sigma (Calc) (mb)g.s. 3 0.882 1 0.8823.08 1 0.204 0.54 0.110164.07 3 0.546 0.2 0.10924.49 1 0.096 0.57 0.05472

Total Sigma (Calc) Total Sigma (Exp)1.16 0.76 mb

nScCad ),( 4948

Cross Section Comparison Between Theory and Experiment

State (MeV) L-value [5] Sigma [4] C2S [5] Sigma (Calc) (mb)g.s. 1 0.059 0.93 0.054872.03 1 0.023 0.98 0.022544.01 3 0.166 0.8 0.13284.03 4 1.648 0.3 0.4944

Total Sigma (Calc) Total Sigma (Exp)0.70 0.50 mb

pCaCad ),( 4948 [5] W.D. Metz et al. Phys. Rev. C Vol. 12, #3 (1975) 827

[3] K.W. Kemper et al. Nucl. Phys. A348 (1980) 339

Highly selected references- Direct Nuclear ReferencesG. R. Satchler, Oxford Science Publications 1983

Study of the (d,p) reaction in the 1p shell J. P. Schifferet al Phys. Rev.164, 1274 (1967)

Systematic extraction of spectroscopic factors from 12C(d,p)and 13C(p,d) reactions X. D. Liu et al Phys. Rev. C69, 064313 (2004)

Comprehensive analysis method for (d,p) stripping reactionsN. Keeley et al Phys. Rev. C69, 064604 (2004)

This is a wonderful time to be in nuclear physics

In the next ten years there will be new acceleratorsbeing commissioned

There will be new detector systems and computing capabilities will continue to increase so that we don’tknow what discoveries will be made, just that there

will be some