- Email: [email protected]
On the induced terms and the partial conservation of the axial vector current in β-decay
PHYSICS
Volume 21, number 6
1 July 1966
LETTERS
ton. This is in contrast with the 5 - and 4- excited states, which may be formed simply by the couplroton orbit (gz) with the ing of the next available pi hole in 207Pb. Since 407Pb is a very good
grateful to Dr. N. Benczer-Koller and M.Bertin for their collaboration in the Coulomb excitation phase and especially for the use of their homegrown detector as well as some of their precious machine time. Finally, we wish to record our appreciation to T.A.Cole and the whole tandem staff for providing the necessary protons after many months of struggle and frustation connected with the installation of an accelerator bearing Serial Number 1.
Z-hole configuration and 206Pb a very good closedshell nucleus [7] *, this experiment can be used to test the validity of the various procedures for the extraction of reduced widths. Specifically, the relative spectroscopic factors for the transitions from the O+-analogue to the first three states of 207~b (p+, f$, pj) should be as 2 5 6 + 4, as becomes clear when writing down the wave function for the 0+ state in 208 Bi. We are currently in-
1. E . C.
Booth and B. Madsen (to be published). 2. C .D. Kavaloski, J. S. Lilley, P. Richard and N. Stein, Phys.Rev. Letters 16 (1966) 807. and F.K. McGowan, Phys. Rev. 99 (1955) 3. P.H.Stelson
vestigating the R-matrix approach in the hope of shedding light on the question of the influence of the interaction radius on the evaluation of the reduced widths. Preliminary results on the scattering of protons from 2MPb indicate a narrower width for the analogue of the ground state of 205Pb, namely 175 f 20 keV. Further work on this nucleus as well as the 207Pb (p, n) reaction is in progress.
112.
4. B. L.Cohen 5. 6.
We enjoyed very helpful discussions with Drs. J . N . Ginocchio, A. M . Lane and D . Robson; we are
7. 8.
indebted to Dr. G. T. Garvey, B. Teitelman, R. Van Bree and M. Wiesen for help in data collection and to Robert Klein for his diligent help with the target preparation. R. Van Bree was also responsible for much of the instrumentation. We are very
and S. W. Mosko, Phys. Rev. 106 (1957) 995; J.Alster, Phys.Rev. 141 (1966) 1138. J.C.Hafele and A.G.Blair, Bull.Am.Phys.Soc.11 (1966) 12. d.C.Carter, W.T.Pinkston and W.W.True, Phys. Rev.120 (1960) 504; V.Gillet, A.M.Green and E.A.Sanderson, Physics Letters 11 (1964) 44. P.Mukherjee and B.L.Cohen, Phys.Rev. 127 (1962) 1284. G.Muellehner and W. C. Parkinson, Bull. Am. Phys. Sot. 11 (1966) 319.
* Very recent experiments and analysis on the reaction 208Pb(d, t)207Pb to these states bear out this statement [8].
*****
ON THE
INDUCED TERMS AND THE AXIAL VECTOR
THE PARTIAL CONSERVATION CURRENT IN B-DECAY
OF
F. KRMPOTId * and D. TADId htitute
nRuder BoSkovW
and Faculty Received
of Science,
University
of Zagreb
20 May 1966
New measurements of 0-d O+ nuclear fi decay seen to indicate the existence of the induced term of the second class in the matrix element of the axial vector current if PCAC is valid.
Besides the elementary particle decay data, nuclear @ decay and b meson capture experiments may also be used to learn some properties of the axial vector current. The axial vector current Ap of the first class under charge conjugation i. e. C A(:) C-l = ApbF) * Fellow of the Consejo National de Investigaciones Cientificas y Tecnicas de la Rep.Argentina. 680
produces the following effective Lagrangian for the single nucleon decay: Lint
= r%kJL - Y5L) - gPfiY5LP +h[W,-VC)PoL+iP
+ uV L](l)
L, L and Lp are bilinear products of lepton wave functions. gA, gp and h are form factors corresponding to the coupling constant, induced pseudo-
PHYSICS
Volume 21, number 6
LETTERS
scalar and induced term of the second class respectively [2-41. On the basis of the C conjugation properties they should all be real. If the interaction among baryons is strictly invariant under isospin symmetry (or SU3) h F Ot . Both gA and gp can be estimated theoretically on the basis of PCAC [6]. As PCAC is a very useful tool in the application of the current-current commutation relations, one would like to have an independent test of it. Using the pion pole dominance assumption [7] and the standard impulse approximation for nuclear p-decay [8] one can write the basic PCAC relation in the form: k
c
sdsr,..
1 July 1966
= (iv2 y5 )/(iy 5) was introduced. The result was again negative. Abandoning PCAC, it was possible [l] to fit the correction factor of I44Pr with rather larger gP. We tried to retain PCAC using h f 0 and succeeded in re reducing the experimental shape factors of Il4Pr and 166Ho with two free parameters X and h = y/2M. The best fits, shown in fig. la and b are obtained for the following values of theprameters: y44Pr (X = -11.1, y = -15.3) and 16 Ho (X = -14.0, y = -9.1). Such a choiche of the parameters rlquires 1(ur) 12 = = 3.37 X 10m4and = 1.59 X lo- for 144Pr and I66Ho respectively to reproduce theft values. These results agree with the result of [4] for the
. d3?-A63(rF) eiksR ‘pf*(yl. . . */A) {y4T*[gAir,y5
c1K
2MgA - -
Y5 kp]]K(Pi(yl*.
.*/A) =
rn$.$
=gld3yl...
d3YA63(YK) eik.R
2Mi?A m; , ~ Vf("/l.. yA) [Tf’vJ%]K
(Pity1 * * *‘Q)
(2)
m;+k”
kC1is the momentum transfer, YK is the coordinate of a single nucleon, pi, (Pf are nuclear wave functions, while the meaning of the other symbols is obvious. After some calculation one obtains the formula valid for p decay and p meson capture 1 (PY5L5(y))= 2$ (Wo - Vc 1 y5L5(y)) + (i ov L5(7:! . W, is the maximal lepton energy and VC is an efCoulomb potential required here on the basis of the gauge invariance argument. It actually measures the change of PCAC due to the electromagnetic interaction. Even if the isospin symmetry is partially lost, the study of field theoretical models [‘I] shows that (2) can still hold provided that the strong coupling constant 1gpp I= (gnn\ . One should also note that (3) is independent of the existence of the h term as its contribution to the derivative of the axial vector current (2) vanishes identically. Using (3) and assuming h G 0, there is only one free parameter X = (iy5)/(ci r) to fit the measured spectrum shape factors of O- - O+ /3 decay transitions. With this parameter it was possible to fit earlier measurements for 144Pr [9] but not recent ones for 144Pr, 166Ho and 144Ce [l]. In order to search for possible nuclear structure effects, I66Ho decay was chosen because of its high ft value. The new parameter n = b2 o r)/(u t) = fective
allowed transitions and 1-1meson capture where y = -7 f 1. This was also supported by the analysis in ref. 10. Analyzing the muon capture rate in the liquid hydrogen a somewhat lower value y = -4, but with the same sign, was obtained [ll] . It is hard to find a theoretical argument for such a large magnitude of y . The medium strong interactions do not induce h in nucleon decay [12]. The only reasonable explanation is due to electromagnetic effects. It is interesting to note that the magnitude and sign of > agree with the Ahrens-Feenberg estimate [13]. The other possibility of fixing this ratio is to make the non-relativistic approximation of (3) resulting in x = - 2k@l
+F2)/Wo - VC)
(4)
where Fl = (1/4&f2r) dVC/‘ddr and F2 is the same function of the effective nuclear shell model potential. Using fi = $* one obtains X w 4 to 5. This is in agreement with earlier measurements of I44Pr B decay [9]. As we do not know how justifiable the nonrelativistic approximation is, it is hard to conclude whether the disagreement with newer measurements [l] contradicts PCAC . It would be extremely useful to get some more experimental evidence on 0- - O+ and O- -+ 2+[15] 6- and 6+ transitions with measurements of the EC/p ratios.
t For the axial vector current
of the second class they are all imaginary, gA and gp being zero in the strict symmetry limit [5].
* In a previous estimation 1141 F2 a 1 was used according to an argument of Konopinski.
681
Volume 21, number
PHYSICS
6
1 July 1966
LETTERS
i
66 -
L-_ 1
20
I
30
1
I
50
L.0
60
rncl
70
20
1
25
L---_.. 30
35
L-AL. W
LO
K
I
L5
rnc2
W pFig.
ls’ig. III.
In.
We are indebted to Professor G. Alaga for several discussions. We have also received some useful information from Dr. H. Daniel, Professor D.Berkyi and Dr. B. Eman.
References 1.
2. 3. 4. 5. 6.
7.
and G.Th.Kaschl, Nuclear Phys.76 (1966) 97. S. Weinberg, Phys.Rev. 112 (1958) 1375. B.Kuchowicz, Acta Phys.Pol.20 (1961) 341; B.Eman and D.TadiC, Nuclear Phys.38 (1962) 453. J.N.Huffaker and E.Greuling, Phys.Rev.132 (1963) 738. N.Cabibbo, Physics Letters 12 (1964) 137. M.Goldberger and S.Treiman, Phys. Rev. 111 (1958) 354; S. L.Adler, Phys.Rev.Letters 14 (1965) 1051; W.I. Weisberger, Phys.Rev. Letters 14 (1965) 1047. M. Gell-Mann and M. 1,evy , Nuovo C imento 16 (1960) 705; M.Gell-Mann, Phys.Rev. 12.5 (1962) 1067. H.Daniel
*****
682
8. B.Stech and I..Schiilkc, %. Physik 179 (1964) 314; C.W.Kim and H.Primakoff, Phys.Rev.139(1963) 1447. 3. R. L.Graham, I.S.Geiger and T.A. Eastwood, Can. J. Phys. 36 (1958) 1084; F.T.Porter and P.P.Day, Phys.Rev.114 (1959) 1286. 10. R. J. Blin-Stoyle and M.Rosina, Nuclear Phys. 70 (1965) 321. 11. A.Fujii and H. Ohtsubo, Progr. Theor.Phys. 34 (1965) 873. 12. M. Ademallo and R. Gatto, Phys .Rev. Letters 13 (1964) 264. 13. T.Ahrens and E.Feenberg, Phys.Rev.86 (1952) 64. 14. D.Tadic, Physics Letters 12 (1964) 176. 15. H. Daniel, G. T. Kaschl, H. Schmid and K. Springer, Phys.Rev.136 (1964) B1240; H. Beekhuis, Physics Letters 21 (1966) 205.
Volume 21, number 6
1 July 1966
LETTERS
ton. This is in contrast with the 5 - and 4- excited states, which may be formed simply by the couplroton orbit (gz) with the ing of the next available pi hole in 207Pb. Since 407Pb is a very good
grateful to Dr. N. Benczer-Koller and M.Bertin for their collaboration in the Coulomb excitation phase and especially for the use of their homegrown detector as well as some of their precious machine time. Finally, we wish to record our appreciation to T.A.Cole and the whole tandem staff for providing the necessary protons after many months of struggle and frustation connected with the installation of an accelerator bearing Serial Number 1.
Z-hole configuration and 206Pb a very good closedshell nucleus [7] *, this experiment can be used to test the validity of the various procedures for the extraction of reduced widths. Specifically, the relative spectroscopic factors for the transitions from the O+-analogue to the first three states of 207~b (p+, f$, pj) should be as 2 5 6 + 4, as becomes clear when writing down the wave function for the 0+ state in 208 Bi. We are currently in-
1. E . C.
Booth and B. Madsen (to be published). 2. C .D. Kavaloski, J. S. Lilley, P. Richard and N. Stein, Phys.Rev. Letters 16 (1966) 807. and F.K. McGowan, Phys. Rev. 99 (1955) 3. P.H.Stelson
vestigating the R-matrix approach in the hope of shedding light on the question of the influence of the interaction radius on the evaluation of the reduced widths. Preliminary results on the scattering of protons from 2MPb indicate a narrower width for the analogue of the ground state of 205Pb, namely 175 f 20 keV. Further work on this nucleus as well as the 207Pb (p, n) reaction is in progress.
112.
4. B. L.Cohen 5. 6.
We enjoyed very helpful discussions with Drs. J . N . Ginocchio, A. M . Lane and D . Robson; we are
7. 8.
indebted to Dr. G. T. Garvey, B. Teitelman, R. Van Bree and M. Wiesen for help in data collection and to Robert Klein for his diligent help with the target preparation. R. Van Bree was also responsible for much of the instrumentation. We are very
and S. W. Mosko, Phys. Rev. 106 (1957) 995; J.Alster, Phys.Rev. 141 (1966) 1138. J.C.Hafele and A.G.Blair, Bull.Am.Phys.Soc.11 (1966) 12. d.C.Carter, W.T.Pinkston and W.W.True, Phys. Rev.120 (1960) 504; V.Gillet, A.M.Green and E.A.Sanderson, Physics Letters 11 (1964) 44. P.Mukherjee and B.L.Cohen, Phys.Rev. 127 (1962) 1284. G.Muellehner and W. C. Parkinson, Bull. Am. Phys. Sot. 11 (1966) 319.
* Very recent experiments and analysis on the reaction 208Pb(d, t)207Pb to these states bear out this statement [8].
*****
ON THE
INDUCED TERMS AND THE AXIAL VECTOR
THE PARTIAL CONSERVATION CURRENT IN B-DECAY
OF
F. KRMPOTId * and D. TADId htitute
nRuder BoSkovW
and Faculty Received
of Science,
University
of Zagreb
20 May 1966
New measurements of 0-d O+ nuclear fi decay seen to indicate the existence of the induced term of the second class in the matrix element of the axial vector current if PCAC is valid.
Besides the elementary particle decay data, nuclear @ decay and b meson capture experiments may also be used to learn some properties of the axial vector current. The axial vector current Ap of the first class under charge conjugation i. e. C A(:) C-l = ApbF) * Fellow of the Consejo National de Investigaciones Cientificas y Tecnicas de la Rep.Argentina. 680
produces the following effective Lagrangian for the single nucleon decay: Lint
= r%kJL - Y5L) - gPfiY5LP +h[W,-VC)PoL+iP
+ uV L](l)
L, L and Lp are bilinear products of lepton wave functions. gA, gp and h are form factors corresponding to the coupling constant, induced pseudo-
PHYSICS
Volume 21, number 6
LETTERS
scalar and induced term of the second class respectively [2-41. On the basis of the C conjugation properties they should all be real. If the interaction among baryons is strictly invariant under isospin symmetry (or SU3) h F Ot . Both gA and gp can be estimated theoretically on the basis of PCAC [6]. As PCAC is a very useful tool in the application of the current-current commutation relations, one would like to have an independent test of it. Using the pion pole dominance assumption [7] and the standard impulse approximation for nuclear p-decay [8] one can write the basic PCAC relation in the form: k
c
sdsr,..
1 July 1966
= (iv2 y5 )/(iy 5) was introduced. The result was again negative. Abandoning PCAC, it was possible [l] to fit the correction factor of I44Pr with rather larger gP. We tried to retain PCAC using h f 0 and succeeded in re reducing the experimental shape factors of Il4Pr and 166Ho with two free parameters X and h = y/2M. The best fits, shown in fig. la and b are obtained for the following values of theprameters: y44Pr (X = -11.1, y = -15.3) and 16 Ho (X = -14.0, y = -9.1). Such a choiche of the parameters rlquires 1(ur) 12 = = 3.37 X 10m4and = 1.59 X lo- for 144Pr and I66Ho respectively to reproduce theft values. These results agree with the result of [4] for the
. d3?-A63(rF) eiksR ‘pf*(yl. . . */A) {y4T*[gAir,y5
c1K
2MgA - -
Y5 kp]]K(Pi(yl*.
.*/A) =
rn$.$
=gld3yl...
d3YA63(YK) eik.R
2Mi?A m; , ~ Vf("/l.. yA) [Tf’vJ%]K
(Pity1 * * *‘Q)
(2)
m;+k”
kC1is the momentum transfer, YK is the coordinate of a single nucleon, pi, (Pf are nuclear wave functions, while the meaning of the other symbols is obvious. After some calculation one obtains the formula valid for p decay and p meson capture 1 (PY5L5(y))= 2$ (Wo - Vc 1 y5L5(y)) + (i ov L5(7:! . W, is the maximal lepton energy and VC is an efCoulomb potential required here on the basis of the gauge invariance argument. It actually measures the change of PCAC due to the electromagnetic interaction. Even if the isospin symmetry is partially lost, the study of field theoretical models [‘I] shows that (2) can still hold provided that the strong coupling constant 1gpp I= (gnn\ . One should also note that (3) is independent of the existence of the h term as its contribution to the derivative of the axial vector current (2) vanishes identically. Using (3) and assuming h G 0, there is only one free parameter X = (iy5)/(ci r) to fit the measured spectrum shape factors of O- - O+ /3 decay transitions. With this parameter it was possible to fit earlier measurements for 144Pr [9] but not recent ones for 144Pr, 166Ho and 144Ce [l]. In order to search for possible nuclear structure effects, I66Ho decay was chosen because of its high ft value. The new parameter n = b2 o r)/(u t) = fective
allowed transitions and 1-1meson capture where y = -7 f 1. This was also supported by the analysis in ref. 10. Analyzing the muon capture rate in the liquid hydrogen a somewhat lower value y = -4, but with the same sign, was obtained [ll] . It is hard to find a theoretical argument for such a large magnitude of y . The medium strong interactions do not induce h in nucleon decay [12]. The only reasonable explanation is due to electromagnetic effects. It is interesting to note that the magnitude and sign of > agree with the Ahrens-Feenberg estimate [13]. The other possibility of fixing this ratio is to make the non-relativistic approximation of (3) resulting in x = - 2k@l
+F2)/Wo - VC)
(4)
where Fl = (1/4&f2r) dVC/‘ddr and F2 is the same function of the effective nuclear shell model potential. Using fi = $* one obtains X w 4 to 5. This is in agreement with earlier measurements of I44Pr B decay [9]. As we do not know how justifiable the nonrelativistic approximation is, it is hard to conclude whether the disagreement with newer measurements [l] contradicts PCAC . It would be extremely useful to get some more experimental evidence on 0- - O+ and O- -+ 2+[15] 6- and 6+ transitions with measurements of the EC/p ratios.
t For the axial vector current
of the second class they are all imaginary, gA and gp being zero in the strict symmetry limit [5].
* In a previous estimation 1141 F2 a 1 was used according to an argument of Konopinski.
681
Volume 21, number
PHYSICS
6
1 July 1966
LETTERS
i
66 -
L-_ 1
20
I
30
1
I
50
L.0
60
rncl
70
20
1
25
L---_.. 30
35
L-AL. W
LO
K
I
L5
rnc2
W pFig.
ls’ig. III.
In.
We are indebted to Professor G. Alaga for several discussions. We have also received some useful information from Dr. H. Daniel, Professor D.Berkyi and Dr. B. Eman.
References 1.
2. 3. 4. 5. 6.
7.
and G.Th.Kaschl, Nuclear Phys.76 (1966) 97. S. Weinberg, Phys.Rev. 112 (1958) 1375. B.Kuchowicz, Acta Phys.Pol.20 (1961) 341; B.Eman and D.TadiC, Nuclear Phys.38 (1962) 453. J.N.Huffaker and E.Greuling, Phys.Rev.132 (1963) 738. N.Cabibbo, Physics Letters 12 (1964) 137. M.Goldberger and S.Treiman, Phys. Rev. 111 (1958) 354; S. L.Adler, Phys.Rev.Letters 14 (1965) 1051; W.I. Weisberger, Phys.Rev. Letters 14 (1965) 1047. M. Gell-Mann and M. 1,evy , Nuovo C imento 16 (1960) 705; M.Gell-Mann, Phys.Rev. 12.5 (1962) 1067. H.Daniel
*****
682
8. B.Stech and I..Schiilkc, %. Physik 179 (1964) 314; C.W.Kim and H.Primakoff, Phys.Rev.139(1963) 1447. 3. R. L.Graham, I.S.Geiger and T.A. Eastwood, Can. J. Phys. 36 (1958) 1084; F.T.Porter and P.P.Day, Phys.Rev.114 (1959) 1286. 10. R. J. Blin-Stoyle and M.Rosina, Nuclear Phys. 70 (1965) 321. 11. A.Fujii and H. Ohtsubo, Progr. Theor.Phys. 34 (1965) 873. 12. M. Ademallo and R. Gatto, Phys .Rev. Letters 13 (1964) 264. 13. T.Ahrens and E.Feenberg, Phys.Rev.86 (1952) 64. 14. D.Tadic, Physics Letters 12 (1964) 176. 15. H. Daniel, G. T. Kaschl, H. Schmid and K. Springer, Phys.Rev.136 (1964) B1240; H. Beekhuis, Physics Letters 21 (1966) 205.