Beta decay general principles
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Beta decay general principles

Beta Decay – General Principles

  • Paul Mantica

  • Lecture 1

  • Euroschool for Exotic Beams

  • Leuven, Belgium - 2009

Beta decay of exotic nuclei science opportunities

Beta Decay of Exotic Nuclei:Science Opportunities

Beta decay properties of unstable nuclei far from stability can provide valuable insight into nuclear shell structure and nuclear deformation changes toward the drip lines.

Precise beta-decay half-lives, end point energies, and branching ratios to unbound states are crucial nuclear physics input parameters for network calculations of the astrophysical rapid neutron capture process.

The selective method of beta decay, in combination with spectroscopic measurements of gamma-rays and neutrons, will open new opportunities to study, for example:

  • Gamow-Teller strength in N~Z nuclei to 100Sn

  • Persistence of shell gaps in extreme neutron-rich nuclei (60Ca, 128Pd)

  • r-process waiting point nuclei along N=82 (124Mo, 123Nb, …) and N=126 (195Tm, 194Er …)

  • E(4+)/E(2+) and phase transitions away from stability (122Pd, 90Ge, 148Xe, …)

  • and others …

Beta decay of exotic nuclei application of fast beams

Beta Decay of Exotic Nuclei:Application of Fast Beams

Significant progress has been made in the measurement of beta-decay properties of exotic nuclei, attributed directly to particle-detection techniques employed with fast beams.

  • Advantage of fast beams:

  • Can correlate implantations and decays event-by-event

    • ID of decay parent

  • suitable for cocktail beams

    • crucial for systematic investigations

  • reduction in background and increased sensitivity

    • half-life: few per day

    • beta-neutron: few per hour

    • beta-gamma: few per minute

Beta decay of exotic nuclei reach across the nuclear chart

Beta Decay of Exotic Nuclei:Reach Across the Nuclear Chart

Beta decay half-lives

All waiting points along N=82 and many along N=126 will be established

First 2+ energies

Major advance in characterizing the systematic variation of E(2+) and E(4+)/E(2+) with increasing neutron number

Beta decay of exotic nuclei experimental needs and observables

Beta Decay of Exotic Nuclei:Experimental Needs and Observables



  • Needs:

  • Fast beams via fragmentation or fission

  • Highly-segmented implantation detector

  • Overall implantation rate < 500 s-1

    • high resolution separator

  • Digital readout (dedicated electronics)

  • Ancillary detectors

    • electrons, neutrons, photons, etc.

  • Floor space: 3 m x 3 m x 3 m

  • Observables:

  • Half-lives

  • Q values (masses)

  • Absolute branching ratios

  • Excited states in daughter nuclei

  • Microsecond isomers

    • excited states in parent


Types of beta decay

Types of Beta Decay

b- decay


EC decay




Proton number

b- decay



Neutron number

Beta decay o bservables

delayed neutron


beta half-lives

delayed gamma rays

Beta Decay Observables

isomer half-lives

isomeric gamma rays









Beta endpoint energy






absolute beta


Beta decay energetics

Beta Decay Energetics

A=204 Mass Chain



Mass = f1(A)Z2+f2(A)Z+f3(A)-d


Beta decay endpoint energy

Beta Decay Endpoint Energy

b- decay

EC decay


Beta energy spectrum

Beta Energy Spectrum

Decay energy is shared between the electron and the neutrino

~1/3 Eb(max)

Energy spectrum is for the positron is continuous up to the endpoint energy

Radioactive decay kinetics

Radioactive Decay Kinetics

Radioactive decay and growth as the form of a first order rate law


No is the initial number of nuclei

Nt is the number of nuclei at time t

e is a mathematical constant 2.7182818284

l is the decay constant

The characteristic rate of a radioactive decay is conveniently given in terms of the half life

t1/2=ln 2/l 0.693/l

The half life is the average time required to reduce the initial number of nuclei by a factor of 2

Radioactive decay curve

Radioactive Decay Curve

Decay rates for beta emission energetics

Decay Rates for Beta Emission:Energetics

There are a wide range of beta decay half lifes:

In general, large decay energies are associated with very short beta-decay half-lives

Rate is proportional to Decay Energy (E0) and Proton Number (Z)

Decay rates for beta emission initial and final states

Decay Rates for Beta EmissionInitial and Final States

However, beta-decay half-lives also depend strongly on the properties of the initial and final states involved in the decay

Beta transition strength is expressed as a product of the energy factor times the half-life (log f0t values).

Allowed beta decay

Allowed Beta Decay

  • Allowed transitions come in two types:

  • Fermi (D=0) and Gamow-Teller (D= 1).

    • Relative orientation of angular momentum vectors for the emitted neutrino and fast electron

  • Log fot is an expression of the transition strength that considers the energy of decay (fovalue) and the time for decay (t), where t is the partial half-life for the decay.

    log fot= log fo+ log t

    log t is the logarithm of the partial half-life of the beta decay

    t = [t1/2]/branch (in seconds)

SuperallowedFermi Decay

Allowed Decay


DJ=0 Dp=no

log ft ~ 3.5

DJ=0,1 Dp=no

log ft ~ 4-7


Gross beta decay theory

Gross Beta Decay Theory

T1/2 a  (Qb - C)-b

a = 2740 s

b = 4.5

Qb = b endpoint energy

C = cutoff energy (pairing gap in daughter)

Sb(E) is the beta-strength function

f is the Fermi function

R is the nuclear radius

Qb is the endpoint energy

Ei is the energy of the final state

  • Gross b decay results overestimate the half-lives of the most neutron-rich isotopes

    • b-decay rate to low-energy states in daughter underestimated

Tachibana et al., Prog. Theor. Phys. 84, 641 (1990)

Pfeiffer, Kratz and Möller, Prog. Nucl. Energy 41, 39 (2002)

Gross theory vs experiment

Gross Theory vs. Experiment

Note that:

Fermi function is dominated by the phase space factor (Qb-Ei)5

The average error increases as T1/2 increases

Inclusion of first forbidden decay (ff) improves average error for longer T1/2 values

Uncertainty in masses far from stability does not dramatically impact T1/2, since relative error does not increase rapidly (Qb is large)

Mölleret al., PRC 67, 055802 (2003)

Beta decay execution at fast beam facilities

Beta Decay – Execution at Fast Beam Facilities

  • Paul Mantica

  • Lecture 2

  • Euroschool for Exotic Beams

  • Leuven, Belgium - 2009

National superconducting cyclotron laboratory

National Superconducting Cyclotron Laboratory

  • 30 Faculty

    • 19 Experimental

    • 7 Theory

    • 4 Accelerator Physics

  • 60 Graduate Students

  • 50 Undergraduate Students

  • 700 member Users Group

  • Selected to design and establish Facility for Rare Isotope Beams (FRIB)

… a world leader in rare isotope research and education




Law school

Nscl coupled cyclotron facility

NSCL Coupled Cyclotron Facility

Projectile fragmentation

Fast-moving projectile is abraded, resulting projectile-like fragment travels with a velocity similar to initial projectile

Produce many isotopes below the initial projectile A and Z, both stable and radioactive

Separation does not depend on the chemical properties of the isotopes

DE 


Projectile Fragmentation

78Kr Fragmentation @ 70 MeV/A

Each fragment can be uniquely identified using time-of-flight, energy-loss, and magnetic rigidity

Rare isotope beam production

Rare Isotope Beam Production

Primary stable atoms are ionized in an ECR source and injected into the accelerating system composed of the coupled K500 and K1200 superconducting cyclotrons




The fast, stable beam is then impinged on a target at the object of the A1900 separator

Rare isotope beam selection

Rare Isotope Beam Selection

The A1900 Fragment Separator is used to select the rare isotope of interest from unwanted fragmentation products

ECR ion sources

  • Dp/p = 5% max

  • Br = 6.0 Tm max

  • 8 msr solid angle

  • 35 m in length






focal plane

Production of 78Ni from 140 MeV/A 86Kr

Morrissey et al., NIM B 204, 90 (2003)

Nscl beta counting system bcs



Planer Ge

NSCL Beta Counting System (BCS)

Implantation detector:

1 each MSL type BB1-1000

4 cm x 4 cm active area

1 mm thick

40 1-mm strips in x and y


6 each MSL type W

5 cm active area

1 mm thick

16 strips in one dimension

Prisciandaroet al., NIM A 505, 140 (2003)

Heavy charged particles

Heavy Charged Particles

Primary interaction is via the electromagnetic interaction between the positive charge of the heavy ion and the negative charge of the orbital electrons within the detection medium.

The maximum energy that can be transferred is


Where m and E are the particle mass and energy, respectively, and me is the electron mass. Since me is much smaller than the incoming particle mass, the energy transfer is small.

primary particle loses its energy over MANY interactions

produce many excited atoms or ion pairs in the detector material

Stopping power

Stopping Power

The linear stopping power for charged particles is given as

Through the Bethe formula, the linear stopping power is a function of the atomic number of the stopping material (Z) and the ion charge (q) and velocity (b=v/c) of the incident particle

Range can be obtained by integrating the energy loss rate along the path of the ion:



Distance of penetration

Range of projectile fragments in silicon

Range of Projectile Fragments in Silicon

Stopping power scales with ion mass, charge and energy:

Scaling can be extended to range calculations:

Practical calculation range of 78 ni in silicon

Practical Calculation:Range of 78Ni in Silicon

The range of 100 MeV/A 78Ni in Si can be scaled from the range of 100 MeV/A alpha particles.

Fast electrons vs heavy ions

Fast Electrons vs. Heavy Ions

Fast electrons lose energy at a lower rate and follow a more torturous path through absorbing materials. This can be attributed to the low ion charge (z = 1) and low mass of the electron.

Fast electrons can also lose energy through radiative processes

S  (1/v)2 NZ (electronic)

S  NEZ2 (radiative)

Therefore the radiative loses are most important for high energy electrons where the absorbing material has a large atomic number.

Range of fast electrons in silicon

Range of Fast Electrons in Silicon

The range of a 10 MeV beta particle in Si is 5.8 g/cm2

r(Si) = 2.33 g/cm3

Therefore, the amount of Si required to fully stop a 10 MeV beta particle is ~ 2.5 cm!

Signal processing for heavy ions and betas in a single silicon detector

Signal Processing for Heavy Ions and Betas in a Single Silicon Detector


beta DE ~ 100’s of keV

beam E ~ 1’s of GeV

CPA16 dual gain preamp from MultiChannel Systems: 16 channels, 50W input impedance, 2V output, ~350 ns rise time.

Low gain: High gain:

0.03 V/pC2.0 V/pC

output to ADCsoutput to Pico Systems 16 ch shaper

Bcs electronics



NIM Trigger

CAMAC Shapers

Digitized waveform: short-lived proton decay of 145Tm

VME Readout

Grzywacz NIMB 204, 649 (2003)


660 channels commissioned and in use with SeGA

BCS Electronics

Conventional BCS Electronics: Block Diagram


Bulk activity measurements


Bulk Activity Measurements

Implant activity into a stopper material for time timplant.

Cease implantation and observe decay for time tdecay.

If necessary, introduce a “clean” stopper material and repeat.

For deposit of a single isotope:


For example


timplant = tdecay=4t1/2

Time correlation of implantations and charged particle decays

Time Correlation of Implantations and Charged-Particle Decays

  • Correlations between an implantation event and subsequent b-decay events are done based on position and time

  • Information regarding the particle ID is carried over to a correlated decay event, therefore, b decays are unambiguously identified

  • Both prompt and delayed g rays can also be unambiguously assigned

  • Decay curves are generated from the difference in absolute times between and implantation and correlated decay event

The high pixel density of the DSSD and low implantation rates (less than 200 ions/second) are essential to reduce probabilities for incorrect correlations





Absolute time

Position (x,y)

Energy loss and time of flight

Fragment total kinetic energy

Gate the g-array ADCs for 20 ms

Absolute time

Position (x,y)

Energy of outgoing particle

Gate the g-array ADCs for 20 ms

Bateman equations

Bateman Equations

The Bateman equations provide a means for analyzing a chain of many successive radioactive decays.

Special assumption: At t=0, only parent is present.

Consecutive first order decays

Consecutive First-Order Decays

For nuclei far from stability, the typical condition is that


This condition is the non-equilibrium case for radioactive decay, and, for a three-generation decay, the number of grand-daughter nuclei will eventually equal the initial number of parent nuclei (assuming the daughter and grand-daughter are not produced directly)



Low counting statistics and the likelihood function

Low Counting Statistics and the Likelihood Function


1 decay observed:

Decay Functions


2 decays observed: 10 scenarios →

3 decays observed: 20 scenarios →


Pereira et al., PRC 79, 035806 (2009)

Background and maximum likelihood

Background and Maximum Likelihood

Background rate was determined uniquely for each 100Sn decay by considering the entire time-lapsed history of implantations into the DSSD

Determination of the 100Sn half-life came from maximizing the likelihood function, considering also those implantation events that were not correlated with a decay

The simulation below shows the close matching between simulated and observed decay rate.

Since N0 depends on l1 itself, an iterative process is used to maximize the function

Beta decay neutron deficient nuclei

Beta Decay – Neutron-Deficient Nuclei

  • Paul Mantica

  • Lecture 3

  • Euroschool for Exotic Beams

  • Leuven, Belgium - 2009

Rp process nucleosynthesis

rp-Process Nucleosynthesis

  • Demonstrated burst conditions [1]

    • T=1.5-2 GK

    • r ~ 106g/cm3

    • lb~ 0.6 s-1

    • lp ~ 10,000 s-1

Termination point

Reactions of rp-process

  • Parameters:

    • b-decay rates

    • (a,g),(p, g) rates

    • Masses

Feeding from (a,p)-process

Schatz et al., NPA 688, 150c (2001)

Challenges with neutron deficient nuclei

Challenges with Neutron-Deficient Nuclei

Selected Fragment: Mo-84

Projectile: 124Xe48+ at 140 MeV/A

Target: 9Be, 305 mg/cm2

Acceptance: 1%

Wedge: 27Al, 180 mg/cm2

Not only is the production of 84Mo overwhelmed by peak production of lighter isotones, but the low-momentum tails of the more prolifically produced, near stable isotopes also dominate the total yield, even with use of a wedge degrader.

Rate in pps/pnA from LISE++

Rf fragment separator

RF Fragment Separator

The RF Fragment Separator was commissioned at NSCL in April 2007. The first beta-decay campaign to study neutron-deficient nuclei was initiated October 2007.

Operating principle:Beam species that have similar Br differ in TOF.

Beam Packets

84 mo production and rffs performance

84Mo Production and RFFS Performance

V = 0 kV

Y slits = 50 mm

Ibeam = 0.8 pnA

83 s-1 over DSSD

V = 47 kV

Y slits = 10 mm

Ibeam = 10 pnA

0.5 s-1 over DSSD

* Rates relative to 84Mo, 5×10-4pps/pnA

** particles/s-pnA

PID are normalized to same number of 80Y implantations

Half life of 84 mo

Half-life of 84Mo

84Mo is a waiting point along the rp-process. The re-measured half-life was found to be more than 1s shorter than the previous value, accelerating mass processing along the rp-process pathway.

Previous T1/2 = 3.7 (+1.0, -0.8) s

Decay curve for 84Mo

T1/2 = 2.2±0.2 s

Half-lives of even-even N=Z nuclei compared with theory

Stoker et al., PRC 79, 015803 (2009)

Correlated 84 mo decays

Correlated 84Mo Decays

Maximum likelihood analysis requires extraction of correlated beta decays.

Correlations were defined for 84Mo by limiting the time window for correlations to less than 20 s after an implantation.

In addition, beta decays that occurred in the same pixel as the implantation, or any of the four nearest-neighbor pixels, were considered.

Three generations of decays were taken into account to generate the likelihood function. The log t between a given 84Mo implantation and the subsequent one, two, and three beta correlations are shown to the right.

The half-life value from the maximum likelihood analysis was consistent with that extracted from the decay curve fit.

Impact of the shorter half life of 84 mo

Impact of the Shorter Half-Life of 84Mo

The order of magnitude uncertainty in the final 84Sr abundance has been reduced to less than a factor of 2 with the new half-life.

A=84 abundances

Previous uncertainty bounded by divergent theoretical T1/2 predictions

(0.8 s lower bound; 6.0 s upper bound)

Schatz et al., Phys. Rep. 294, 167 (1998)

Delayed proton emission

Delayed Proton Emission

For nuclei with Z > N, the proton drip line is located where the proton separation energy equals zero

Neutron-deficient nuclei near the proton drip line typically have large QEC values, and beta decay can directly populate proton unbound states.

The “delayed” protons will be emitted with the apparent half-life of the beta decay.


Statistical treatment of delayed proton emission

Statistical Treatment of Delayed Proton Emission

When the level density of the proton unbound states in the daughter is smaller than the resolution of the particle detector, the individual protons cannot be distinguished. A statistical treatment of the proton spectrum can then be applied.

Need GT matrix element <s>, level densities r, and transmission coefficient for proton decay Tℓ

Huang et al.,PRC 59, 2402 (1999)

Delayed protons from 81 zr decay

Delayed Protons from 81Zr Decay

Delayed gamma rays

Delayed protons

Termination of the rp process

Termination of the rp Process

Known ground state alpha emitters among the neutron-deficient Te isotopes result in the theoretical termination of the rp process with the Sn-Sb-Te cycle.

Decay data in the vicinity of the doubly-magic nucleus 100Sn is critical to the characterization of the nuclear structure effects in this region of the nuclear chart.

Sn-Sb-Te cycle. The solid lines indicate reaction flows of more than 10%.

Schatz et al.,PRL 86 3471 (2001)

Gamow teller beta decay of 100 sn

Gamow-Teller Beta Decay of 100Sn

Simple shell model calculation would predict GT decay to a single pg9/2-1ng7/2+1 state in 100In with B(GT) = 17.8

2p-2h admixtures in both the 100Sn initial and the 100In final states will fragment the B(GT), but most of the strength is still expected to reside within the Qb window

100Sn → 100In

The calculation to the right considers such mutliparticle-multihole admixtures. The lowest 1+ state in 100In is predominantly 1p1h, but the B(GT) is reduced by a factor of 4.

Extraction of B(GT) for 100Sn requires accurate determination of T1/2 and branching ratios to final states in 100In

Brown and Rykaczewski, PRC 50, R2270 (1994)

Beta decay of 102 sn

Beta Decay of 102Sn

2800 102Sn nuclei

Both high resolution and calorimetric g-ray detection

T1/2 = 3.8(2) s; QEC = 5.76(14) MeV

Faestermannet al., EPJ A 15, 185 (2002)

Karnyet al., EPJ A 25, s01, 135 (2005)

B gt hindrance factors

B(GT) Hindrance Factors

102Sn: B(GT) = 4.2(9)

Hindrance Factor h

h(102Sn)= 3.7

Karnyet al., EPJ A 25, s01, 135 (2005)

What is known about 100 sn

What is Known About 100Sn?


  • GANIL [Lewitowiczet al., PLB 322, 20 (1994)]

    • 112Sn at 63 MeV∙A onto a 144 mg/cm2 Ni target

    • 11 events attributed to 100Sn48+ in 44 hours

    • cross section for 100Sn ≥ 120 pb

  • GSI [Schneider et al., ZPA 348, 241 (1994)]

    • 124Xe at 1095 GeV∙A onto a 6 g/cm2 Be target

    • 9 events attributed to 100Sn50+ in 277 hours

    • cross section for 100Sn ~11 pb


  • GSI [Summereret al., NPA 616, 341c (1997)]

    • 6 events followed by subsequent b decay

    • T1/2 = 0.94 (+0.54, -0.27) s

    • Qb = 7.2 (+0.8, -0.5) MeV

    • B(GT) = 11.3 (+6.5, -8.3) assuming all decay to a single 1+ state in 100In





Radio frequency fragment separator

Radio Frequency Fragment Separator

  • Radio Frequency Fragment Separator (RFFS)

Purification of neutron-deficient beams by time-of-flight

  • 1.5-m long RF cavity, Vmax=100 kV

  • First campaign in Fall 2008

  • Beam rejection factor of >200 for 100Sn

NSF MRI PHY-05-20930

Production of 100 sn

Production of 100Sn

  • Only the third time 100Sn was ever produced and studied.

Primary beam dose of 6.7 x 1016112Sn ions over 11.5 days

  • Production rate of 100Sn and other N=Z nuclei was below EPAX predictions

Bazinet al., PRL 101, 252501 (2008)

Half life of 100 sn 98 in 96 cd

Half-life of 100Sn, 98In, 96Cd

Log(time) curves

  • The half-lives of the ground states of heavy N=Z nuclei were deduced by event-by-event decay correlation measurements and analyzed based on a maximum likelihood probability function. The new values are:

    • 96Cd: 1.3 (+0.24, -0.21) s

    • 98In: 0.047 (13) s

    • 100Sn: 0.55 (+0.70, -0.31) s

Comparison with theory

Bazinet al., PRL 101, 252501 (2008)

Ground state of 101 sn

Ground State of 101Sn

  • Ground state spin and parity of 101Sn up for debate

  • 7/2+ from Darby et al. [next presentation]

    • a decay fine structure

  • 5/2+ from Seweryniaket al., PRL 99, 022504 (2007).

    • g-ray correlated with protons from 101Sn decay

Z=50 isotopes

N=51 isotones

101 sn beta delayed proton decay

101Sn Beta-Delayed Proton Decay

The b-delayed proton spectrum from 101Sn is strongly influenced by the angular momentum of the ground state

Factor of 4 improvement in statistics over previous measurement. Shape of spectrum more consistent with the model-dependent statistical treatment assuming 5/2+ ground state spin and parity

Lorussoet al., PoS (NiC-X) 172 (2008)

Kavatsyuket al., EPJ A 31, 319 (2007)

Other nscl b p results

Other NSCL bp Results

Delayed proton emission observed for first time in 98,99In and 96Cd

Approved experiments to study bp and other decay modes in much lighter, neutron-deficient nuclei

Fermi beta decays along n z

Fermi Beta Decays along N=Z

All N=Z odd, odd nuclei above A=75 have very short (< 100 ms) b-decay half-lives

Several of these nuclides have two b-decaying states

Short half-lives indicative of superallowed Fermi 0+ 0+b decays

  • Open questions:

  • Do the states with short b half-lives correspond to the ground states of the parents?

  • Are there b-decaying isomers in 82Nb and 86Tc?

  • What is the ground-state to ground-state branching ratio for the short-lived b decays?

* Assumes 0.5% branching to non-analog states.

Isomer and b-delayed g-ray spectroscopy on odd-odd, N=Z nuclides with A > 80.

Faestermannet al., EPJ A 15 185 (2002)

Beta decay neutron rich nuclei

Beta Decay – Neutron-Rich Nuclei

  • Paul Mantica

  • Lecture 4

  • Euroschool for Exotic Beams

  • Leuven, Belgium - 2009

Delayed neutron emission

Delayed Neutron Emission

For nuclei with N > Z, the neutron drip line is located where the neutron separation energy equals zero

Neutron-rich nuclei near the proton drip line typically have large Qb- values, and beta decay can directly populate neutron unbound states.

The “delayed” neutrons will be emitted with the apparent half-life of the beta decay.

Parallels delayed proton emission…

Tensor interaction and monopole shift of single particle orbitals

Tensor Interaction andMonopole Shift of Single-Particle Orbitals

j> =  + 1/2

pf7/2 fills

j< = – 1/2

pg9/2 fills






  • In general:

    • Radial wavefunctions must be similar

    • Large  and ´ enhance tensor monopole effect



Otsukaet al., PRL 95, 232502 (2005)

Sn region of the nuclear chart

Sn Region of the Nuclear Chart

Z 




N 




















Proton single particle energy shift in 51 sb isotopes

Proton Single-Particle Energy Shift in 51Sb Isotopes

proton g7/2 orbital “moves” relative to proton d5/2 when neutron h11/2 orbital is occupied

Attractive monopole interaction

Attractive Monopole Interaction

Proton-neutron interaction is strongest when the orbitals they occupy strongly overlap. This overlap is maximum when n ~ p. The attractive nature of the monopole interaction may lead to a re-arrangement of the single-particle orbitals.





In 51Sb, a change in the proton single-particle states is observed upon filling of the h11/2 neutron orbital.

















Shell model calculations with the gxpf1 effective interaction

Shell Model Calculations with the GXPF1 Effective Interaction

Ca (Z=20)

Removal of protons from f7/2 orbital produces significant energy gap between nf5/2 and np1/2orbitals at Ti (Z=22) and Ca (Z=20)

Ti (Z=22)

  • Two questions to be addressed:

  • Is there evidence for an N=34 subshell closure in Ca?

  • How are the neutron spe’s evolving with changing proton number?

Honmaet al., PRC 65, 061301(R) (2002)

E 2 and shell closures







E(2+) and Shell Closures

The excitation energy of the first excited 2+ state in even-even nuclei can provide initial insight into the degree of nuclear collectivity

Nuclear shapes within a major shell

Nuclear Shapes within a Major Shell





Systematic variation of 66 dy 2 and 4 states

Systematic Variation of 66Dy 2+ and 4+ states

3.3 for rigid rotor




Systematic variation of e 2

Systematic Variation of E(2+)

pf7/2 fills

pf7/2 fills

Excited states in 54Ca34 have remained elusive!

Production of neutron rich ca isotopes

Production of Neutron-Rich Ca Isotopes

Primary beam: 76Ge 130 MeV/nucleon

Momentum Acceptance: 5%

300 mg/cm2 Al wedge at I2 position

Br1,2 = 4.3867 Tm

Br3,4 = 4.1339 Tm

Target 352 mg/cm2 Be

16 hours

Br1,2 = 4.4030 Tm

Br3,4 = 4.1339 Tm

Target 352 mg/cm2 Be

167 hours

Decay curves for 53 56 ca

Decay Curves for 53-56Ca





Mantica et al., PRC 77, 014313 (2008)

53 56 ca t 1 2 comparison to theory

53-56Ca T1/2 Comparison to Theory

(No N=32,34 gaps)

(N=32,34 gaps)

Shell Model

Gross Theory


No discrimination between theoretical treatments at N=34

Honmaet al., PRC 69, 034335 (2004)

Segmented germanium array sega

Segmented Germanium Array (SeGA)

16-detector SeGA arrangement – 24 cm i.d.

Warm FETs

Resolution < 3.5 keV at 1.3 MeV

Stopped beam experiments

Mueller et al., NIM A 466, 492(2003)

54 ca beta delayed gamma rays

54Ca Beta-Delayed Gamma Rays

Delayed gamma rays

T1/2 = 86±7 ms

Qb = 10.33±0.79 MeV (sys.)















Decay curve gated on delayed gamma rays

Beta decay branching ratios

Beta-Decay Branching Ratios

  • Absolute intensities for gamma-ray transitions are obtained from the following:

  • Number of parent nuclei correlated with beta decay

  • Number of detected gamma rays

  • Gamma array peak efficiency curve

For the 247-keV transition in 54Ca

No = 136

Ng = 23

Ig(abs) ~ 100%

eg = 14%

log fot = log fo + log tpartial

Eb(max) = Qb – Ex

= 10.33 MeV -0.28 MeV

= 10.05 MeV

Direct feeding to the ground state determined from missing absolute gamma-ray intensity.

tpartial = t1/2/branch

= 0.086 s/1.0

= 0.086 s

In the case of the decay of 54Ca, the apparent beta feeding all proceeds through the excited state at 247 keV.

log fot = 4.25±0.18

Pandemonium effect

Pandemonium Effect

Hardy et al., PLB 71, 307 (1977)

509 discrete g rays

The word “apparent” was purposefully used in the description of the beta feeding following the decay of 54Ca. Note that the Qb value is more than 10 MeV. There is the likelihood of the presence of higher-energy with intensities below detection threshold. These unobserved transitions will impact the calculated branching ratios.

QEC = 8.91 MeV

4.2 MeV

Only Ig > 1% shown

Gierliketal., NPA 724, 313 (2003)

Delayed neutrons can help

Delayed Neutrons Can Help…

Neutron-rich nuclei will have Qb values that fall above Sn in the daugher nucleus. Therefore, detection of neutrons with high efficiency can offset the impact of unobserved gamma rays on calculated beta branches.

T1/2 = 86±7 ms

Qb = 10.33±0.79 MeV (sys.)



Simultaneous neutron and gamma measurements are not straightforward, as both demand high solid angle coverage, but require different active media for efficient detection.


Sn = 4.6±0.5 MeV

discrete gamma rays





R process elemental abundances

r-Process Elemental Abundances

  • Nuclear properties (e.g. mass) determine r-process yields

  • Predicted r-process yields do not match observations

  • Need masses, half-lives, and neutron branchings



Nucleosynthetic process in Type II supernovae(?) or neutron star mergers(?)

Rapid neutron captures on seed nuclei followed by b- decays

Path on neutron-rich side of stability

K.-L. Kratz ISOLDE Workshop, CERN, Geneva, Dec. 15 - 17, 2003

Neutron rich ni and co isotopes

Neutron-Rich Ni and Co Isotopes

Time between arrival and decays:

r-process nuclei

Energy loss in Si (Z)



time (ms)





Result for half-life: 110 +100-60 ms

Compare to theoretical estimate used:470 ms

Time of flight (m/q)

MSU – Mainz – LANL – Maryland – Notre Dame

Neutron emission ratio observer nero

3He Proportional



24.8 cm

11.2 cm

19.2 cm

13.6 cm





BF3 Proportional


Neutron Emission Ratio Observer (NERO)

NERO consists of 44 BF3 and 16 3He proportional counters.

NERO efficiency ~45% to 1 MeV

Lorussoet al., PoS (NIC-IX), 243 (2006)

Pn and t 1 2 for neutron rich cu and ni

Pn and T1/2 for Neutron-Rich Cu and Ni

QRPA Moeller et al. 1997

QRPA Moeller et al. 2003

CQRPA Borzov 2005

OXBASH Lisetzky et al.

This work

Previous work

120 rh 75 beta delayed neutrons

120Rh75 Beta-Delayed Neutrons

Can use combination of T1/2 and Pn to isolate ground state deformation

Small neutron branching observed for 120Rh decay not consistent with macroscopic models that include an ad-hoc quenching of the N=82 shell closure

Pn 5.4%

Montes et al., PRC 73, 035801 (2006)

P n determined from gamma rays

Pn Determined from Gamma Rays

The delayed gamma-ray spectra from 55Sc and 56Sc have “identical” transitions with energies 592 and 1204 keV: Provides evidence for delayed neutron emission following decay of 56Sc.

The absolute gamma ray intensities can be used to deduce Pn; however, this will be a lower limit, since the calculation only considers neutron transitions that populate excited states in the A-1 daughter.

Complicated decays 56 sc

Complicated Decays: 56Sc

56Sc has two β-decaying states: a short-lived, low-spin state and a longer-lived high spin states. 56Sc also has a microsecond isomer that decays by several prompt gamma rays.

Beta decay future @ frib

Beta Decay – Future @ FRIB

  • Paul Mantica

  • Lecture 4

  • Euroschool for Exotic Beams

  • Leuven, Belgium - 2009

Facility for rare isotope beams frib

Facility for Rare Isotope Beams(FRIB)

MSU selected to design and establish FRIB at the present NSCL site

Frib location on the msu campus

FRIB Location on the MSU Campus

Scientific goals of frib drive specifications

Scientific Goals of FRIB Drive Specifications

  • FRIB with 400 kW for all beams and minimum energy of 200 MeV/u will have beam rates for some isotopes up to 100 times higher than other facilities

  • For example: FRIB intensity will allow the key benchmark nuclei 54Ca (reaccelerated beams) and 60Ca (fast beams) to be studied

Experimental areas

Experimental Areas

  • A full suite of experimental equipment will be available for fast, stopped and reaccelerated beams

  • New equipment

    • Stopped beam area (LASERS)

    • ISLA Recoil Separator

    • Solenoid spectrometer

    • Active Target TPC

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