EXPERIMENTS WITH LARGE GAMMA DETECTOR ARRAYS Lecture V

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EXPERIMENTS WITH LARGE GAMMA DETECTOR
ARRAYSLecture V

• Ranjan Bhowmik
• Inter University Accelerator Centre
• New Delhi -110067

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MEASUREMNENT OF NUCLEAR LIFETIMES
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NUCLEAR LIFE TIME

• The transition probability for g-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 Eg and multipolarity
? .
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Weisskopf Single Particle Estimate
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.
ELECTRIC
MAGNETIC
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Weisskopf Estimate
T in seconds Eg in keV A in Atomic Mass Unit
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Nuclear Quadrupole Deformation

• For deformed nuclei, the deformation b 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
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Measurement of nuclear life times

• A collection of nuclei produced at t0 would
  decay according to the law N(t) N0 exp(- t /
  t) for mean life time t
• t 1/l where l is the total transition
  probability
• If t gt ns, it can be measured by direct timing
  with a Ge detector using the following techniques
  
• Irradiation counting ( gt min)
• Tagged spectroscopy ( gt ms)
• Pulsed beam technique ( ns - ms)
• g-g 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)

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Irradiation Counting

• Life times gt 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
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Recoil Tagged Spectroscopy

• In Recoil Tagged Spectroscopy, recoil products
  transported to low-background area using recoil
  separator
• Time difference between arrival of recoil
  g-decay measured with TAC
• Suitable for life-times ms -ms range

PRC 70 (2004) 014311
Transport Time ms
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Pulsed beam Spectroscopy

• Beam is bunched or chopped to a width lt t
• Repetition rate 100 ns - ms or longer
• Out of beam g-spectra recorded
• Exponential decay during "beam off period"

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Pulsed Beam Technique
Eg 221 384 keV 6 ms Isomer
CHOPPED BEAM 2 ms ON 100 ms OFF
PRC55(1997)620
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Pulsed Beam Technique
BEAM OFF Period g-g coincidence 384 keV gate
PRC55(1997)620
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Short Half Lives

• Exponential decay folded by detector resolution
• Centroid shift Method
• For short decay time, compare centroid for
  delayed g with centroid for prompt g of similar
  energy

PRC65(2002)027301
Shift in centroid is equal to the mean life t of
the level
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g- g Coincidence

• For DC beam, g-g 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
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Multi coincidence method

• Poor time resolution of Ge limitation t gt ns
  isomers
• Excellent energy resolution compared to
  scintillators
• Fast scintillators available for timing with g or
  b particles ( Dt lt 500 ps)
• Fast plastic for detection of b
• BaF2 for g-detection ( Dt 300 ps)
• Ge with good energy resolution used for channel
  selection, other two for g-g or b-g timing
• Applicable for g-g-g or b-g-g coincidences with
  Ge-BaF2-BaF2 or plastic-Ge-BaF2
• NIM280(1989)49

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g- g - g Coincidence
J.of.Phys.G31 (2005)S1421
Ge-BaF2-BaF2 coincidence allows channel selection
by Ge and timing by BaF2 Can we do pulsed
beam-g-g coincidence ?

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

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LIFETIME MEASUREMENT BY INDIRECT METHODS

• Nuclei produced in heavy ion induced fusion have
  large recoil velocities 0.01 -0.02c
• For v/c 0.01 recoils travel 1mm in 3 ps
• Can be used to provide a time scale ps in terms
  of distance of travel
• Distinguish g-emission from stopped or in-flight
  recoils by the Doppler energy shift of g-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)

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Recoil Distance Doppler Shift ( RDDS or RDM)

• Thin target 500 mg/cm2
• Recoils decay in flight
• Stopped by a thick foil known as Plunger
• g-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

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RDM Technique

• Doppler shift for detector at q

• Intensity of in-flight component

• Intensity of stopped component

• Ratio of the two

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Recoil Distance Plunger Setup

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

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g-Spectrum from RDM
PRC66(2002)064318
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RDM Decay Curve

• Distance measured to ?0.1 m 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

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Multi-level decay

• Three level decay where I3 decays exponentially
  to I2 and I2 has a life time t2
• N3(t) N0 exp(-t/t3)
• dN2/dt dN3/dt - N2/t2
• growth feeding decay
• N3(t) a expt(-t/t2) b exp(-t/t3)
• "Effective decay time" would depend on both t2
  t3
• Decay curves for preceding transitions have to be
  measured

t3 50 ps t2 varied
t2 50 ps t3 0-150 ps
T.K. Alexander and J.S. Forster, Adv. Nucl.
Phys. 10 (1979) 197.
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Bateman Equation

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

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
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Data Analysis for RDM

• LIFETIME 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

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Differential Decay Curve Method (DDCM)

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

Z. Physik. 334(1989)163

• Since all intensities are directly measured
  lifetime can be extracted
• Most sensitive to data for 0.5t lt t lt 2t
• Main uncertainty from unobserved transitions

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COINCIDENT DDCM

• Peak to background in Plunger experiments can be
  improved by gating with an auxiliary detector.
  Neutron array gating for proton-rich nuclei
• Large g-array allow coincidence measurements in
  coincidence with other transitions in cascade
• Considerable clean up of spectrum in g-g
  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
  possible

B
A
Z. Physik. 334(1989)163
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COINCIDENT DDCM
t"
t'
T
B
0
A
A decays
Target
Plunger
B decays
TIME

• Probability of detecting both B A
• IBA ? ? NB(t') exp-lA(t" t') dt' dt"
• with the conditions
• t', t" gtT both unshifted t',t" ltT both
  shifted
• t' lt T t" gtT shifted ? unshifted

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COINCIDENT DDCM

• There are four variations of this technique
• Gating from Top ( A to be measured)
• Total Gate (su) removes background
  side-feeding
• Narrow Gate (s) direct lifetime measurement
• Gating from Bottom (B to be measured)
• Total Gate (su) reduces background
• Narrow 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.
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DDCM with Gating from TOP
EPJA26(2005)153

• Gating by the shifted component from top

36?
independent of feeding lifetime GASP
Array 40Ca(40Ca,a2p)74Kr Large Doppler Shift
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DDCM 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
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Doppler Shift Attenuation Method (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

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LINESHAPE PROGRAM

• DECHIST
• Simulate the slowing down history of the
  recoils in backing Get v(t) and qR(t) as a
  function of time
• HISTAVER
• From the velocity history, calculate the
  Doppler shift observed at angle qg as a
  function of time
• LINESHAPE
• Calculate the population Ni(t) of the state by
  solving Bateman equations.
• Simulate the energy spectrum in a g-detector
  from the time dependence of Ni(t)
• Compare with actual shape and iterate for
  minimum ?2

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DSAM Lineshape for 58Cu
PRC63(2000)021301
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Side 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

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Energy Correlated DSAM

• In g - g - time correlation, the second gamma is
  emitted with probability exp(-Dt/tB)
• tB lifetime of B
• Putting narrow gate on T1 measures tB directly
• Time spectra for g1 with narrow gate on T2
  sensitive to lifetime tA
• Insensitive to feeding of tA

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Narrow Gate on Top (NGT)
NIMA437(1999)274

• Side-feeding top-feeding effects eliminated

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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
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Fractional Doppler Shift

• SD bands have very large Qt with lifetime lt 100
  fs
• g-emission before significant slowing down of the
  recoils
• Large Doppler shift with angle
• Fractional Doppler Shift F(t) ltbgt/b0

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Fractional Doppler Shift
PRL76 (1996) 3510

• Top of band show full velocity F(t) 1
• Middle of the band has F(t) 90
• Slower transitions in the bottom of the band have
  F(t) lt 80
• Extract average Quadrupole moment of the band by
  comparing with simulation

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Fractional Doppler Shift
Q0 8 eb
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