Log ft values in Beta Decay

Filip G. KondevFilip G. Kondevkondev@anl.govkondev@anl.gov

2nd Workshop for DDEP Evaluators, Bucharest, Romania

May 12-15,2008

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Some useful references Books

“Week interaction and nuclear beta decay”, H.F. Schopper, 1966

“Handbook of nuclear spectroscopy”, J. Kantele, 1995

“Radiation detection and measurements”, G.F. Knoll, 1989

“Alpha-, Beta- and Gamma-ray Spectroscopy”, Ed. K. Siegbahn, 1965

Journal ArticlesW. Bambynek et al., Rev. Mod. Phys. 49 (1977) 77

N.B. Gove and M.J. Martin, Nuclear Data Tables 10 (1971) 205

S. Raman and N.B. Gove, Phys. Rev. C7 (1973) 1995

B. Singh et al., Nuclear Data Sheets 84 (1998 487 Plenty of information available on the Web

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Beta Decay: universal term for all weak-interaction transitions between two neighboring isobars

Introduction

Takes place is 3 different formsEC (capture of an atomic electron)

: n p + e- +

: p n + e+ +

a nucleon inside the nucleus is transformed into another

EC: p + e- n +

4

Iii

Iff

SLII fi Lfi )1(

)(~)( llL

orssS 0

1)(~)(

allowed

forbidden

when the angular momentum conservation

requires that Ln >0 and/or if=-1

1,0 fi IIIwhen L=n=0 and if=+1

L = n defines the degree of forbiddenness (n)

Classification ofdecay transition

5

0+1

+

Fermi

0S0L

0 fi III

)1( fiGamow-Teller

0+0

+

0L 1S or1 fi III

2+2

+0 fi III 0iI

mixed Fermi & Gamow-Teller

Classification of allowed decay

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Type of transition Order of forbiddenness

I if

Allowed 0,+1 +1

Forbidden unique1234.

2345.

-1+1-1+1.

Forbidden1234.

0, 1234.

-1+1-1+1.

Classification of decay transitions

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The fifth power beta decay rule:

the speed of a transition increases approximately in proportion to the fifth power of the total transition energy (if other things are being equal, of course)

depends on spin and parity changes between the initial and final state

additional hindrance due to nuclear structure effects – isospin, “l-forbidden”, “K-forbidden”, etc.

52])1()([1

cZMZM

If

Ii

Some useful empirical rules

8

iP

TTt i

exp2/1

2/1

W

eneeeendWCWZFWWWp

g

T 1

203

2

2/1

),()(2

2ln

partial half-life of a given (+,EC) decay branch (i)

g – week interaction coupling constant

pe – momentum of the particle

We – total energy of the particle

W0 – maximum energy of the particle

F(Z,We) – Fermi function – distortion of the particle wave function by the nuclear charge

Cn – shape factor

Z – atomic number

decay lifetime

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W

eneeeen dWCWZFWWWpf1

220 )/)(,()(

tfg

T

THF nn

ni

2ln2 3

22

2/1

2/1

contains the nuclear matrix elements

2

statistical rate function (phase-space factor): the energy & nuclear structure dependences of the decay transition

decay Hindrance Factor

10

coming from experiment

tfft logloglog

coming from calculations

Decay Mode

Type I (if) log f

EC + allowed 0, +1

(+)

EC + 1st-forb unique

2 (-)

0log f

)/log(log 010 fff

)log( 00 ff EC

N.B. Gove and M. Martin, Nuclear Data Tables 10 (1971) 205

)]/()log[( 0011 ffff ECEC

Log ft values

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Log f ENSDF analysis program LOGFT – both Windows & Linux distribution http://www.nndc.bnl.gov/nndcscr/ensdf_pgm/analysis/logft/ LOGFT Web interface at NNDChttp://www.nndc.bnl.gov/logft/

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Log t

iP

TTt i

exp2/1

2/1

)]()([ inIoutIP tottot

i

i

iTi

tot IinoutI )1()/(

2

2

1

)2()1()21(

EM

EM TTT

What we want to know accurately

T1/2, I, T &

)10(78.0)619416( totI

)16(086.0)721521( totI

In

Out

= 0.69(10)(net

)

31.6log][10056.20022.0 6 tst 386.2log f 7.8log ft

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There are only a few cases where unambiguous assignment can be made

“pandemonium effect” – neutron rich nuclei – log ft is a just lower limit!

needs to know the decay scheme and its properties accurately!

Rules for Spin/Parity Assignments

~1000 cases

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B. Singh, J.L. Rodriguez, S.S.M. Wong & J.K. Tuli

~3900 cases -> gives centroids and widths

Log ft values – latest review

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Implications for DDEP evaluations

aft logi

P

TTt i

exp2/1

2/1

iPaTf logloglog exp

2/1

aPTfi logloglog exp

2/1

42 108.3105.1 i

P

)8(5.9log fta

39.2log f49.2log exp

2/1 T

from systematics

from calculationsfrom experiment

)8(012.0)(exp tPi

16

0+

2+

4+

6+

8+

7-

K~0K~0

j=R

K=7K=7

j

j

j

large angular momentum re-orientation

First forbidden 5 < log ft <10

log ft =20

log ft =19

T1/2 =3.8x1010 y

…but be careful, nuclear structure is important

K-forbidden decay