EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V

EXPERIMENTS WITH LARGE EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYSGAMMA DETECTOR ARRAYS

Lecture VLecture V

Ranjan Bhowmik

Inter University Accelerator Centre

New Delhi -110067

Lecture V SERC-6 School March 13-April 2,2006 2

MEASUREMNENT OF NUCLEAR MEASUREMNENT OF NUCLEAR LIFETIMESLIFETIMES


NUCLEAR LIFE TIMENUCLEAR LIFE TIMEThe transition probability for -decay is related to the overlap between initial and final state wave functions:

B is the reduced transition probability related to the nuclear matrix elements. Measuring the lifetime gives the information about nuclear matrix elements B(R)

The life time is also dependent on photon energy E and multipolarity .


Weisskopf Single Particle EstimateWeisskopf Single Particle Estimate

).()(

33

!)!12(

)1(2);( 2

22

2kckR

ce

lll

lWeisskopfElT l

fi

).()(

33

!)!12(

)1(20);( 2

222

2kckR

ce

McRlll

lWeisskopfMlT l

fi

ELECTRIC

MAGNETIC

A crude estimate of the Matrix elements has been given by V.F. Weisskopf assuming single particle wave functions for the nucleons. Matrix elements are usually presented in Weisskopf units to indicate whether they are single particle or collective in nature.


Weisskopf EstimateWeisskopf Estimate

T in seconds

E in keV

A in Atomic Mass Unit


Nuclear Quadrupole DeformationNuclear Quadrupole Deformation

For deformed nuclei, the deformation is related to the intrinsic Quadrupole moment Q0

Q0 is related to B(E2) for collective E2 transitions

Lifetime is related to Q0 by the expression:


Measurement of nuclear life timesMeasurement of nuclear life times

A collection of nuclei produced at t=0 would decay according to the law : N(t) = N0 exp(- t / ) for mean life time

whereis the total transition probability

If > ns, it can be measured by direct timing with a Ge detector using the following techniques :

Irradiation & counting ( > min)Tagged spectroscopy ( > s)Pulsed beam technique ( ns - ms) coincidence ( ns - 100 ns)

For shorter lifetimes, an indirect method has to be used:RDM ( ps - ns)DSAM ( 100 fs - ps) FDS ( 10-100 fs)


Irradiation & CountingIrradiation & Counting

Life times > 1 min Sample is irradiated to produce

the isomer Taken to low-background area Counted using a Ge-detector

Life times ~ sec - min

Fast transport system: Rabbit or Gas-jet-recoil-transport

Repeated irradiations to increase statistics

PRC37(1988)2894


Recoil Tagged SpectroscopyRecoil Tagged Spectroscopy In Recoil Tagged Spectroscopy, recoil products transported to

low-background area using recoil separator Time difference between arrival of recoil & -decay measured

with TAC Suitable for life-times s -ms range

PRC 70 (2004) 014311

Transport Time ~ s


Pulsed beam SpectroscopyPulsed beam Spectroscopy

Beam is bunched or chopped to a width <

Repetition rate 100 ns - s or longer

Out of beam-spectra recorded

Exponential decay during "beam off period"


Pulsed Beam TechniquePulsed Beam Technique

PRC55(1997)620

E = 221 & 384 keV6 s Isomer

CHOPPED BEAM2 s ON100 s OFF


Pulsed Beam TechniquePulsed Beam Technique

PRC55(1997)620

BEAM OFF Periodcoincidence384 keV gate


Short Half LivesShort Half Lives

Exponential decay folded by detector resolution

Centroid shift Method

For short decay time, compare centroid for delayed with centroid for prompt of similar energy

PRC65(2002)027301

Shift in centroid is equal to the mean life of the level


CoincidenceCoincidence

For DC beam, coincidence technique can be used for locating isomers

Gates on transitions above & below the isomer Does not depend on the side-feeding from other isomers

NPA601(1996)195


Multi coincidence methodMulti coincidence method

Poor time resolution of Ge limitation > ~ns isomers Excellent energy resolution compared to scintillators Fast scintillators available for timing with or

particles ( t < 500 ps)Fast plastic for detection of BaF2 for -detection ( t ~ 300 ps)

Ge with good energy resolution used for channel selection, other two for or timing

Applicable for or coincidences with Ge-BaF2-BaF2 or plastic-Ge-BaF2

NIM280(1989)49


CoincidenceCoincidence

Lifetime of 627 keV level of 48V : T1/2 ~ 77 ps

J.of.Phys.G31 (2005)S1421Ge-BaF2-BaF2

coincidence allows channel selection by Ge and timing by BaF2

Can we do pulsed beam- coincidence ?


LIFETIME MEASUREMENT BY LIFETIME MEASUREMENT BY INDIRECT METHODSINDIRECT METHODS

Nuclei produced in heavy ion induced fusion have large recoil velocities ~ 0.01 -0.02c

For v/c = 0.01 recoils travel 1m in 3 ps Can be used to provide a time scale ~ ps in terms of

distance of travel Distinguish -emission from stopped or in-flight recoils

by the Doppler energy shift of -rays emitted in flight Lifetime measurement using Doppler shift :

Recoil Distance Doppler Shift (RDDS) ( 1 ps - 1 ns )

Doppler Shift Attenuation Method ( 100 fs - 1 ps)

Fraction Doppler Shift ( 5 - 50 fs)


Recoil Distance Doppler ShiftRecoil Distance Doppler Shift ( RDDS or RDM) ( RDDS or RDM)

Thin target ~ 500 g/cm2

Recoils decay in flight Stopped by a thick foil

known as Plunger -rays detected both

from in-flight and those stopped in Plunger

Difference in intensity of two components measured as a function of target-stopper distance


RDM TechniqueRDM Technique

Doppler shift for detector at

Intensity of in-flight component

Intensity of stopped component

Ratio of the two


Recoil Distance Plunger SetupRecoil Distance Plunger Setup

Thin target ( ~ 500 g/cm2) stretched wrinkle-free Stopper (Au) stretched foil parallel to target Linear motor for changing target-stopper distance


-Spectrum from RDM-Spectrum from RDM

PRC66(2002)064318


RDM Decay CurveRDM Decay Curve

Distance measured to 0.1 by computer control

Absolute target-stopper distance calibrated by capacitance measurement

Distance scale converted to time scale from average recoil velocity

Multiple exponential decay components

Feeding from states above with comparable life times


Multi-level decayMulti-level decay

3 = 50 ps2 varied

T.K. Alexander and J.S. Forster, Adv. Nucl. Phys. 10 (1979) 197.

Three level decay where I3 decays exponentially to I2 and I2 has a life time 2

N3(t) = N0 exp(-t/3)

dN2/dt = dN3/dt - N2/2

growth feeding decay

N3(t) = expt(-t/2) + exp(-t/3) "Effective decay time" would

depend on both 2 & 3

Decay curves for preceding transitions have to be measured

2 = 50 ps3 = 0-150 ps


Bateman EquationBateman Equation

For a level being fed from multiple levels, the relation between the intrinsic lifetime i of the level and the apparent lifetime is given by Bateman Equation :

iij

jji NN

dtdN

In a cascade of transitions the decay of topmost transition is fitted by an exponential and the time evolution of subsequent levels calculated.

Intensities of the un-shifted and shifted peak:

t

is

t

iu

dttNtI

dttNtI

0

)()(

)()(


Data Analysis for RDMData Analysis for RDM

LIFETIMELIFETIME program J.C. Wells, ORNL1985

Input : Shifted & un-shifted peak intensities for the cascade Trial values of lifetimes Trial value of Side-feeding lifetime Global search for least square minimization

Output:

Lifetimes of the states in the cascade

Main uncertainty due to insufficient knowledge of side-feeding


Differential Decay Curve Method Differential Decay Curve Method (DDCM)(DDCM)

The Bateman equations can be reformulated in terms of the observed un-shifted intensity Iu for different stopper distances

iuj

ju

iu

i IIdtdI Z. Physik. 334(1989)163

• Since all intensities are directly measured lifetime can be extracted

• Most sensitive to data for 0.5 < t < 2• Main uncertainty from unobserved transitions


COINCIDENT DDCMCOINCIDENT DDCM Peak to background in Plunger experiments can be improved by

gating with an auxiliary detector. Neutron array gating for proton-rich nuclei

Large -array allow coincidence measurements in coincidence with other transitions in cascade

Considerable clean up of spectrum in coincidence Gating from below equivalent to normal RDM Gating from above completely removes side-feeding Three components in B-A coincidence

Due to time ordering of transitions Ius is not possibleBAuu

BAsu

BAss

BA IIII

B

A

Z. Physik. 334(1989)163


COINCIDENT DDCMCOINCIDENT DDCM

Probability of detecting both B & A :

IBA = NB(t') exp[-A(t" – t')] dt' dt"

with the conditionst', t" >T ; both unshifted t',t" <T ; both shiftedt' < T ; t" >T shifted unshifted

B

A

Target PlungerB decays

A decays

t' t"T0

TIME


COINCIDENT DDCMCOINCIDENT DDCM

There are four variations of this technique : Gating from Top ( A to be measured)

Total Gate (s+u): removes background & side-feedingNarrow Gate (s) : direct lifetime measurement

Gating from Bottom (B to be measured)Total Gate (s+u) : reduces backgroundNarrow Gate (u) : reduced sensitivity to feeding of B

For the second case ( Gate on the Shifted peak of top transition) lifetime of A can be measured directly from the observed coincident intensities without solving Bateman equations.


DDCM with Gating from TOPDDCM with Gating from TOP

Gating by the shifted component from top :

36

)()(1xIvxI

BAssdx

d

BAsu

EPJA26(2005)153

independent of feeding lifetime

GASP Array40Ca(40Ca,2p)74KrLarge Doppler Shift


DDCM with gating from TOPDDCM with gating from TOP

Consistent value of lifetime obtained over the region of sensitivity

Other Variations: Thin stopper followed by

recoil detector for gating Thin stopper foil to slow

down recoils followed by a thick one to stop

Allows dIss/dx to be measured directly

Isu

Iss


Doppler Shift Attenuation Method Doppler Shift Attenuation Method (DSAM)(DSAM)

Thin target backed by high Z stopper material to stop recoils in ~ ps time scale

Line-shape profile depends on nuclear lifetime Short life time: full shift Long life time : No shift


LINESHAPE PROGRAMLINESHAPE PROGRAM DECHIST

Simulate the slowing down history of the recoils in backing; Get v(t) and R(t) as a function of time

HISTAVER

From the velocity history, calculate the Doppler shift observed at angle as a function of time

LINESHAPE

Calculate the population Ni(t) of the state by solving Bateman equations.

Simulate the energy spectrum in a -detector from the time dependence of Ni(t)

Compare with actual shape and iterate for minimum 2


DSAM Lineshape for DSAM Lineshape for 5858CuCu

PRC63(2000)021301


Side feeding ModelSide feeding Model

Side feeding lifetimes comparable to cascade life times

Simulated by a Rotational cascade side feeding model

Side-feeding lifetime decreases as we go up in energy


Energy Correlated DSAMEnergy Correlated DSAM In time

correlation, the second gamma is emitted with probability exp(-t/

= lifetime of B Putting narrow gate on T1

measures directly Time spectra for 1 with

narrow gate on T2 sensitive to lifetime A

Insensitive to feeding of A


Narrow Gate Narrow Gate on Top (NGT)on Top (NGT)

Side-feeding & top-feeding effects eliminated

NIMA437(1999)274


Narrow gate Below (NGB)Narrow gate Below (NGB) Shifted component reduced in intensity Change in shape of the DSAM spectrum with narrow gate

below used to extract lifetime

NIMA417 (1998)150


Fractional Doppler ShiftFractional Doppler Shift

SD bands have very large Qt with lifetime < 100 fs -emission before significant slowing down of the recoils Large Doppler shift with angle

Fractional Doppler Shift F() = <>/0



PRL76 (1996) 3510

Top of band show full velocity F() ~1

Middle of the band has F() ~ 90%

• Slower transitions in the bottom of the band have F() < 80%

• Extract average Quadrupole moment of the band by comparing with simulation



Q0~ 8 eb

EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V

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