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Parity non-conservation in low energy nucleon-nucleon interaction
Volume 122B, number 5,6
PIIYSICS LETTERS
17 March 1983
PARITY NON-CONSERVATION IN LOW ENERGY NUCLEON-NUCLEON INTERACTION G. N A R D U L L I , G. P R E P A R A T A , E. SCRIMIER! Dipartimento di Fisica dell'Universit~ di Bari, Bari, Italy and L~¢FN, Sezione di Bari, Italy
and J. S O F F E R Centre de l'hysique Th~orique, ~-VRS Marseille, France
Received 29 November 1982
We apply a recently proposcd theory of parity violation effects in the wave function of nucleons to the derivation of the parity violating (I'V) nuclcon-nuclcon potential. We obtain PV terms in tim hamiltonian much larger than previously calculated. A successful application of such potential is made to the calculation of the proton asymmetry at low energies.
In a recent paper [1], hereafter referred to as I, it has been shown that the large parity-violating (PV) effects observed in high energy nucleon .nucleon scattering 121 can be explained by a peculiar PV admixture induced in the nucleon wave function (WF) by the usual, AS = 0. weak non-leptonic hamiltonian. Accordingly tire tW effects are gene.atcd by the interference of the strong amplitude, fig. la, with the weak diagram, fig. I b, wherc the weakly interacting boson of the standard model (W e , Z 0) are exchanged among the quarks comprising the polarized nucleon. The el¢ W',
Z °
feet of the insertion of the weak non-leptonic, parity violating, strangeness conserving hamiltonian, HPV=0, on the nucleon's leg has been calculated in I using a standa,d dispersive approach that has proven effective in dealing with non-leptonic kaon decays [31. Let us now briefly recall the results of this calculation. One starts from an effective hamiltonian, written in terms of the nucleon fields and a few other fields, which is k n o w n to describe correctly a given strong interaction process. The effect of the insertion of H P ~ = 0 (fig. l b) a m o u n t s to adding to the effective hamiltonian a new piece of the form 6H = i~75C,I , ,
(1)
where 3'5 = (0 1), q, is the nucleon field and C is the 2 X 2 matrix C = CNrO + A r 3 ,
(2)
with N'
CN --~ 2 X 10-6
N'
(a)
(b)
Fig. 1. Graphs containing to NN' -, f scattering: (a) contains strong interactions only; (b) is the weak diagram containing PV wave function admixture. N is a polarized nucleon, N' an unpolarized one and f is the final state. 0 0 3 1 - 9 1 6 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 03.00 © 1983 North-Holland
A"
-0.1X
10 - 6 .
(3,4)
The theoretical uncertainty on both nunrbers have been estimated about 2 0 - 3 0 % [ 1 ]. It has been shown in 1 that the large PV admixture induced in the nucleon wave function by eqs. ( 1 ) - ( 4 ) predicts a satisfactory value for the a s y m m e t r y found 329
Volume 122B, number 5,6
PIIYSICS LETTERS
in the high energy p r o t o n - w a t e r scattering [2]. The same effect has been recently studied [4] for nucleon nucleon scattering at intermediate energies (Plab ~ 1.5 - 3 G e V / c ) and predictions have been made for the a s y m m e t r y in the cross section for the two different proton helicities r~ The aim of this paper is to provide an answer to the following question: what is the PV effect induced by the previous WF admixture in low energy n u c l e o n nucleon interaction? And m particular: does this effect explain the small values of the asynmtetries observed at low energies ~2 (1;-< 100 MeV)? For if the answer turns out to be negative, it would cast serious doubts on our understanding of the A S = 0 weak non-leptonic interaction. The starting point of our analysis of low energy nucleon - n u c l e o n interaction is the following effective (parity conserving) interaction hanrihonian: /lln T =
ig, N~l,"t. ~75(I, + goN~p[7u
X • "'I'P u
+ (Xv/2M)
+gwN~[7 la + ( X s / 2 M )
ou~'~,]
oU~a~] ,l~cou, (5)
which in the non-relativistic limit generates a one boson exchange potential (OBEP) which takes into account tire mare features of the nucleon - n u c l e o n interaction, i.e. the long range attractive part (the 7r contribution) and the short range repulsive term (the co- O contribution). As for the intermediate raqge attraction in the OBE framework it is supplied by a hypothetical s-wave resonance, the o ~3, whereas in o t h e r approaches [12] it arises from the exchange o f two pkms (the two pion exchange potential, TPEP). In view o f the elusiveness of a o, having the characteristics needed to produce a reasonable medium range attraction, we prefer to folh)w the latter approach and choose for the different coupling constants in eq. (5) the values q u o t e d in ref.
[121: g2N/4rr =
14.4,
g2oN/4rr= 4.65
,
(6,7)
Xs = - 0 . 1 2 .
(8,9)
17 March 1983
Let us briefly discuss these numbers. Eqs. (7)--(9) originate from the usual arguments of vector meson d o m i n a n c e (VMD) and SU(3) synmretry, llad one used o-exchange, one would have needed larger values for gwN and goN; on the other hand if the TPEP is preferred the given values turn out to be adequate [12], F u r t h e r m o r e from the measured leptonic width of p and co one could obtain somewhat smaller (about 10%) for gpN and g ~ N t 4 Adding now the PV contribution (1) to the full hamiltonian, and redefining as in I the nucleon fields by the rotation = e x p ( - ~ O"I5) ,!,,
(10)
we obtain a PV piece in the interaction h a m i h o n i a n which can be easily c o m p u t e d as ~s. H PV = 2
-l/2FTr fa(~ AX) 3
+lll'~'i×v (°uv/eM)
"/S (* ^ avPu)3 ~)
+ } (H0 , . p u +111 ° p~) ,rut 5 f i t w+ o + ~a( Hlr3)Yu75 ~cou
(11)
with /4; = .V,'22 AgwN ,
(12)
HO=CNgpN,
HI=H2'=AgpN,
(13,14)
HO=CNgwN,
tll=Agoo N.
(15,16)
F r o m e q s . ( l 1 ) - ( 1 6 ) one obtains the low energy nuc l e o n . - n u c l e o n parity violating potential V PV by going to the non-relativistic limit. According to the above discussion we must also include the parity violating potential induced by the first term m eq. (11) in the TPEP [14,15] ~6. Thus we have V PV = V~r + V/2 + V~ + V2n ,
(17)
where:
!
gON = ~gwN
Xv = 3.7 ,
*l It is worth mentioning that the prediction of ref. [41 for pp-scattering at Plab = 1.5 GeV/c are within the range of tile preliminary results recently reported by a Los Alamos experimenl [51. 12 l:or a recent review see ref. [6]. Relevant theoretical work appears in refs. [ 7 - 1 0 I. 4 a For a review of this approach see ref. [ l l ]. 330
;4 Even though the accuracy of the VMD prediction is not clear yet, tile VMD values should be in the right ball park. ) s We follow as closely as possible the notation of ref. [ 101. Our conventions on metrics and "r-matrices are those of ref.[13]. 6 We include only the AI = 1 part of the TPEP PV potential. As for the d~l = 0, 2 parts existing calculations [ 16] are not totally reliable [ 17 ].
Volume 122B, number 5,6
Vw =
PHYSICS LETTERS
2-l/2iF~r(g~rN/2M)('tl ^~2)3(~tl +°'2)
x [p,t~(r)]_ ,
(is)
1 I V ° = (gtjN/M)[H(o}'tl "lr 2 + ~H~(I:I + x2)3] X {(o"l
.)
- (griN/M) I t 1 ½(~1 - ~ 2)3(°"1 + 02) (P' f ( r ) } , +(goN/M)II,
1~1
~(~1 A~2)3(~1 + ~ 2 ) [ P ' f ( r ) ]
- , (1o)
X [(o"l
+HL~(~I
)"(r)]_ ]
f = <~(-)1 vPVI ~(+)),
" 't2)3(O'1 + ~ 2 ) { P , f ( r ) } + } '
"(20)
where 1
P = 2(Pl
P2) ,
f,r(r) = exp(--m~rr)/4nr , f(r) = exp(--mpr)/47rr . As far as V27r is concerned it consists of several terms; we report here only those which are relevant to ppscattering: V2rr = V B + V C .
2/;~('c 1 +1r2)3(a I
a 2 ) { p , fB(r)) + ,
VC = - 2 1 ~ ( ~ 1 + H ) 3 i(ot ^ ~ 2 ) [ P , - t c ( r ) l -
,
(26)
is the weak amplitude which we calculate by sandwiching the potential (17) between cigenstates of the parity conserving hamihonian. Computing the distorted waves by use of the Reid soft core potential, modified by Pieper [18], one obtains: Ap = - 0.014 goN(Ho0 + H 1 ) - 0.004 gwN(HOw + H I )
+ 0.11 F . .
(:7)
(22)
From this expression we see that at low energy the asymmetry is determined by a sum of two contributions both of the order of 10 - 7 but of different signs (negative for pco exchange, positive for 2rr exchange). Introducing the numerical values reported above, we obtain
(23)
Ap"-5X
(21)
with V t~ =
(25)
where F is the parity conserving hadronic amplitude and
~2){p,f(r)}+
+ i(1 + Xs)(O'l A a 2 ) [ p ,
(24)
[Or,(+ ), Op( ) being the elastic cross section l\)r longitudinally polarized protons with helicity + and respectively], at 15 MeV. Following ref. [7] we calculate the PV scattering amplitude in the distorted-wave Born approxintation, i.e. we write for tile full scattering amplitude: 1,'.r = F + f ,
= (g,.oN/M) ([H 0 + I I 1 / 2 M ( x 1 + ~t2)3 I
V
In order to have an idea of the phenomenological implications of eqs. (12) - (23) we calculate the asymntetry A p = l o p ( + ) - O p ( - - ) ] / [ O p ( + ) + Op(- )]
n2){p,f(r)} +
+ i(l + Xv)[al ^ a 2 l [ p , f ( r ) ]
17 March 1983
fB and f(. being superpositions of Yukawa potentials whose explicit form can be found in ref. [15]. Eqs. ( 11 ) - ( 2 3 ) describe the effect of parity violating admixtures in the nucleon wave function on the n u c l e o n - n u c l e o n potential. According to the above discussion such potential should be added to the contributions arising from a few other mechanisms, that have been studied in the literature [6,10]. Wc should, however, note that in view of the large size of the calculated coupling constants (12) (16), parity violation in the low energy nucleon- nucleon interaction appears to bc substantially dominated by the WF effect. In particular the large value o f F n [eq. (12)1 makes the consideration of the PV 2n exchange potential V2n necessary in any calculation of parity violation in nuclear physics.
10 - 7
[Exp.(
1.7-+0.85) X 10-7I
(28)
(experimental value from ref. [19]), which, in view of the theoretical uncertainties we have emphasized and of the cancellation between two large contributions. is indeed rather satisfying. It is interesting to note that had we used nucleon potentials different from the Reid soft core potential, we would have obtained substantially different results :7 As a matter of fact it seems quite generally true, not only in low energy n u c l e o n - n u c l e o n scattering but also in other nuclear processes, including the famous thertnal neutron radiative capture [20], that PV effects depend in a very critical way on details of the parity t7 A comparison among the effects of different strong potentials on parity violation at low energy is in ref. 18].
331
Volume 122B, number 5,6
PIIYSICS LETI'ERS
conserving potential that are not discriminated by the reformation coming from N -N phase shifts and nuclear properties. This remarkable fact makes it conceivable that parity violation may b e c o m e an independent tool to extract and understand the fundamental n u c l e o n nucleon interaction. To conclude, we have derived the effect o f PV admixture in the nucleon WF in the PV n u c l e o n - n u c l e o n potential. The effect appears much larger than different, previously calculated, contributions and emphasizes the importance o f parity violation coming from two pion exchange. The substantial parity violation found in the n u c l e o n - n u c l e o n potential renders the actual observable effects very sensitive to details of the parity conserving interaction previously unexplored, thus suggesting parity violation as a new tool Io clarify and understand poorly known aspects of the nuclear interaction.
References [1 [ G. Nardulli and G. Preparata, Phys. Lett. 117B (1982) 445. [21 N. Lockyer ctal., Phys. Rev. Lctt. 45 (1980) 1821. [3] G. NarduUi and G. Preparata, Phys. Lett. 104B (19811 399; G. Nardulli, G. Prcparata and D. Rotondi, preprint BA-GT 82/11, to be published in Phys. Rev. D.
332
17 March 1983
[4] G. Nardulli, E. Scrimicri and J. Softer, preprint CPT82/P. 1420, to be published in Z. Phys. C. [5] D. Nagle, Talk 5th Intern. Syrup. on High energy spin physics (Brookhaven, USA. 1982). 16] M. Simonius, Talk 5th Intern. Syrup. on Iligh energy spin physics (Brookhaven, USA, 1982). [7] V.R. Brown, E.M. Henley and F.R. Krejs, Phys. Rev. C9 (1974) 935. [8] B.H.J. McKellar and K.R. Lassey, Phys. Rev. C17 (19781 842. 19] 13. Dcsplanques and J. Missimer, Nucl. Phys. A300 (1978) 286; B. Dcsplanques, Nucl. Phys. A335 (198(I) 147. 110] B. Desplanqucs, J.F. Donoghuc and B.R. Holstein, Ann. Phys. (NY) 124 (19801 449. [ 11 ] K. Erkelcnz, Phys. Rcp. 13C (1974) 193. [12] W.N. Cottingham, M. Lacombe, B. Loiseau, J.M. Richard and R. Vinh Mau, Phys. Rcv. D8 (1973) 800; R. Vinh Mau, J.M. Richard, B. Loiseau, M. Lacombe and W.N. Cottingham, I'hys. Lett. 44B (1973) 1. [ 13] J.D. Bjorken and S.D. Drell, Relativistic quantum fields (McGraw-ttill, New York, 1965). [14] H.J. Pirner and D.O. Riska, Phys. Lctt. 44B (1973) 151. [ 15] B. Desplanques, Phys. l.ett. 41B (1972) 461. [ 161 R.J. Blin Stoylc, Phys. Rev. 118 (19601 1605; R. Lacaze. Nucl. Phys. B4 (19681 657. [ 17] M. Gari, Phys. Rep. 6C (19731 317. [18] R.V. Reid Jr., Ann. Phys. 50 (1968) 411; S.C. Pieper, Phys. Rev. C9 (1974) 883. [ 19] D. Nagle et al., All' Conf. Proc. N.51 (American Institutc of Physics, New York, 19781 p. 224. [201 V.M. Lobashov et al., Nucl. Phys. A197 (19721 241.
PIIYSICS LETTERS
17 March 1983
PARITY NON-CONSERVATION IN LOW ENERGY NUCLEON-NUCLEON INTERACTION G. N A R D U L L I , G. P R E P A R A T A , E. SCRIMIER! Dipartimento di Fisica dell'Universit~ di Bari, Bari, Italy and L~¢FN, Sezione di Bari, Italy
and J. S O F F E R Centre de l'hysique Th~orique, ~-VRS Marseille, France
Received 29 November 1982
We apply a recently proposcd theory of parity violation effects in the wave function of nucleons to the derivation of the parity violating (I'V) nuclcon-nuclcon potential. We obtain PV terms in tim hamiltonian much larger than previously calculated. A successful application of such potential is made to the calculation of the proton asymmetry at low energies.
In a recent paper [1], hereafter referred to as I, it has been shown that the large parity-violating (PV) effects observed in high energy nucleon .nucleon scattering 121 can be explained by a peculiar PV admixture induced in the nucleon wave function (WF) by the usual, AS = 0. weak non-leptonic hamiltonian. Accordingly tire tW effects are gene.atcd by the interference of the strong amplitude, fig. la, with the weak diagram, fig. I b, wherc the weakly interacting boson of the standard model (W e , Z 0) are exchanged among the quarks comprising the polarized nucleon. The el¢ W',
Z °
feet of the insertion of the weak non-leptonic, parity violating, strangeness conserving hamiltonian, HPV=0, on the nucleon's leg has been calculated in I using a standa,d dispersive approach that has proven effective in dealing with non-leptonic kaon decays [31. Let us now briefly recall the results of this calculation. One starts from an effective hamiltonian, written in terms of the nucleon fields and a few other fields, which is k n o w n to describe correctly a given strong interaction process. The effect of the insertion of H P ~ = 0 (fig. l b) a m o u n t s to adding to the effective hamiltonian a new piece of the form 6H = i~75C,I , ,
(1)
where 3'5 = (0 1), q, is the nucleon field and C is the 2 X 2 matrix C = CNrO + A r 3 ,
(2)
with N'
CN --~ 2 X 10-6
N'
(a)
(b)
Fig. 1. Graphs containing to NN' -, f scattering: (a) contains strong interactions only; (b) is the weak diagram containing PV wave function admixture. N is a polarized nucleon, N' an unpolarized one and f is the final state. 0 0 3 1 - 9 1 6 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 03.00 © 1983 North-Holland
A"
-0.1X
10 - 6 .
(3,4)
The theoretical uncertainty on both nunrbers have been estimated about 2 0 - 3 0 % [ 1 ]. It has been shown in 1 that the large PV admixture induced in the nucleon wave function by eqs. ( 1 ) - ( 4 ) predicts a satisfactory value for the a s y m m e t r y found 329
Volume 122B, number 5,6
PIIYSICS LETTERS
in the high energy p r o t o n - w a t e r scattering [2]. The same effect has been recently studied [4] for nucleon nucleon scattering at intermediate energies (Plab ~ 1.5 - 3 G e V / c ) and predictions have been made for the a s y m m e t r y in the cross section for the two different proton helicities r~ The aim of this paper is to provide an answer to the following question: what is the PV effect induced by the previous WF admixture in low energy n u c l e o n nucleon interaction? And m particular: does this effect explain the small values of the asynmtetries observed at low energies ~2 (1;-< 100 MeV)? For if the answer turns out to be negative, it would cast serious doubts on our understanding of the A S = 0 weak non-leptonic interaction. The starting point of our analysis of low energy nucleon - n u c l e o n interaction is the following effective (parity conserving) interaction hanrihonian: /lln T =
ig, N~l,"t. ~75(I, + goN~p[7u
X • "'I'P u
+ (Xv/2M)
+gwN~[7 la + ( X s / 2 M )
ou~'~,]
oU~a~] ,l~cou, (5)
which in the non-relativistic limit generates a one boson exchange potential (OBEP) which takes into account tire mare features of the nucleon - n u c l e o n interaction, i.e. the long range attractive part (the 7r contribution) and the short range repulsive term (the co- O contribution). As for the intermediate raqge attraction in the OBE framework it is supplied by a hypothetical s-wave resonance, the o ~3, whereas in o t h e r approaches [12] it arises from the exchange o f two pkms (the two pion exchange potential, TPEP). In view o f the elusiveness of a o, having the characteristics needed to produce a reasonable medium range attraction, we prefer to folh)w the latter approach and choose for the different coupling constants in eq. (5) the values q u o t e d in ref.
[121: g2N/4rr =
14.4,
g2oN/4rr= 4.65
,
(6,7)
Xs = - 0 . 1 2 .
(8,9)
17 March 1983
Let us briefly discuss these numbers. Eqs. (7)--(9) originate from the usual arguments of vector meson d o m i n a n c e (VMD) and SU(3) synmretry, llad one used o-exchange, one would have needed larger values for gwN and goN; on the other hand if the TPEP is preferred the given values turn out to be adequate [12], F u r t h e r m o r e from the measured leptonic width of p and co one could obtain somewhat smaller (about 10%) for gpN and g ~ N t 4 Adding now the PV contribution (1) to the full hamiltonian, and redefining as in I the nucleon fields by the rotation = e x p ( - ~ O"I5) ,!,,
(10)
we obtain a PV piece in the interaction h a m i h o n i a n which can be easily c o m p u t e d as ~s. H PV = 2
-l/2FTr fa(~ AX) 3
+lll'~'i×v (°uv/eM)
"/S (* ^ avPu)3 ~)
+ } (H0 , . p u +111 ° p~) ,rut 5 f i t w+ o + ~a( Hlr3)Yu75 ~cou
(11)
with /4; = .V,'22 AgwN ,
(12)
HO=CNgpN,
HI=H2'=AgpN,
(13,14)
HO=CNgwN,
tll=Agoo N.
(15,16)
F r o m e q s . ( l 1 ) - ( 1 6 ) one obtains the low energy nuc l e o n . - n u c l e o n parity violating potential V PV by going to the non-relativistic limit. According to the above discussion we must also include the parity violating potential induced by the first term m eq. (11) in the TPEP [14,15] ~6. Thus we have V PV = V~r + V/2 + V~ + V2n ,
(17)
where:
!
gON = ~gwN
Xv = 3.7 ,
*l It is worth mentioning that the prediction of ref. [41 for pp-scattering at Plab = 1.5 GeV/c are within the range of tile preliminary results recently reported by a Los Alamos experimenl [51. 12 l:or a recent review see ref. [6]. Relevant theoretical work appears in refs. [ 7 - 1 0 I. 4 a For a review of this approach see ref. [ l l ]. 330
;4 Even though the accuracy of the VMD prediction is not clear yet, tile VMD values should be in the right ball park. ) s We follow as closely as possible the notation of ref. [ 101. Our conventions on metrics and "r-matrices are those of ref.[13]. 6 We include only the AI = 1 part of the TPEP PV potential. As for the d~l = 0, 2 parts existing calculations [ 16] are not totally reliable [ 17 ].
Volume 122B, number 5,6
Vw =
PHYSICS LETTERS
2-l/2iF~r(g~rN/2M)('tl ^~2)3(~tl +°'2)
x [p,t~(r)]_ ,
(is)
1 I V ° = (gtjN/M)[H(o}'tl "lr 2 + ~H~(I:I + x2)3] X {(o"l
.)
- (griN/M) I t 1 ½(~1 - ~ 2)3(°"1 + 02) (P' f ( r ) } , +(goN/M)II,
1~1
~(~1 A~2)3(~1 + ~ 2 ) [ P ' f ( r ) ]
- , (1o)
X [(o"l
+HL~(~I
)"(r)]_ ]
f = <~(-)1 vPVI ~(+)),
" 't2)3(O'1 + ~ 2 ) { P , f ( r ) } + } '
"(20)
where 1
P = 2(Pl
P2) ,
f,r(r) = exp(--m~rr)/4nr , f(r) = exp(--mpr)/47rr . As far as V27r is concerned it consists of several terms; we report here only those which are relevant to ppscattering: V2rr = V B + V C .
2/;~('c 1 +1r2)3(a I
a 2 ) { p , fB(r)) + ,
VC = - 2 1 ~ ( ~ 1 + H ) 3 i(ot ^ ~ 2 ) [ P , - t c ( r ) l -
,
(26)
is the weak amplitude which we calculate by sandwiching the potential (17) between cigenstates of the parity conserving hamihonian. Computing the distorted waves by use of the Reid soft core potential, modified by Pieper [18], one obtains: Ap = - 0.014 goN(Ho0 + H 1 ) - 0.004 gwN(HOw + H I )
+ 0.11 F . .
(:7)
(22)
From this expression we see that at low energy the asymmetry is determined by a sum of two contributions both of the order of 10 - 7 but of different signs (negative for pco exchange, positive for 2rr exchange). Introducing the numerical values reported above, we obtain
(23)
Ap"-5X
(21)
with V t~ =
(25)
where F is the parity conserving hadronic amplitude and
~2){p,f(r)}+
+ i(1 + Xs)(O'l A a 2 ) [ p ,
(24)
[Or,(+ ), Op( ) being the elastic cross section l\)r longitudinally polarized protons with helicity + and respectively], at 15 MeV. Following ref. [7] we calculate the PV scattering amplitude in the distorted-wave Born approxintation, i.e. we write for tile full scattering amplitude: 1,'.r = F + f ,
= (g,.oN/M) ([H 0 + I I 1 / 2 M ( x 1 + ~t2)3 I
V
In order to have an idea of the phenomenological implications of eqs. (12) - (23) we calculate the asymntetry A p = l o p ( + ) - O p ( - - ) ] / [ O p ( + ) + Op(- )]
n2){p,f(r)} +
+ i(l + Xv)[al ^ a 2 l [ p , f ( r ) ]
17 March 1983
fB and f(. being superpositions of Yukawa potentials whose explicit form can be found in ref. [15]. Eqs. ( 11 ) - ( 2 3 ) describe the effect of parity violating admixtures in the nucleon wave function on the n u c l e o n - n u c l e o n potential. According to the above discussion such potential should be added to the contributions arising from a few other mechanisms, that have been studied in the literature [6,10]. Wc should, however, note that in view of the large size of the calculated coupling constants (12) (16), parity violation in the low energy nucleon- nucleon interaction appears to bc substantially dominated by the WF effect. In particular the large value o f F n [eq. (12)1 makes the consideration of the PV 2n exchange potential V2n necessary in any calculation of parity violation in nuclear physics.
10 - 7
[Exp.(
1.7-+0.85) X 10-7I
(28)
(experimental value from ref. [19]), which, in view of the theoretical uncertainties we have emphasized and of the cancellation between two large contributions. is indeed rather satisfying. It is interesting to note that had we used nucleon potentials different from the Reid soft core potential, we would have obtained substantially different results :7 As a matter of fact it seems quite generally true, not only in low energy n u c l e o n - n u c l e o n scattering but also in other nuclear processes, including the famous thertnal neutron radiative capture [20], that PV effects depend in a very critical way on details of the parity t7 A comparison among the effects of different strong potentials on parity violation at low energy is in ref. 18].
331
Volume 122B, number 5,6
PIIYSICS LETI'ERS
conserving potential that are not discriminated by the reformation coming from N -N phase shifts and nuclear properties. This remarkable fact makes it conceivable that parity violation may b e c o m e an independent tool to extract and understand the fundamental n u c l e o n nucleon interaction. To conclude, we have derived the effect o f PV admixture in the nucleon WF in the PV n u c l e o n - n u c l e o n potential. The effect appears much larger than different, previously calculated, contributions and emphasizes the importance o f parity violation coming from two pion exchange. The substantial parity violation found in the n u c l e o n - n u c l e o n potential renders the actual observable effects very sensitive to details of the parity conserving interaction previously unexplored, thus suggesting parity violation as a new tool Io clarify and understand poorly known aspects of the nuclear interaction.
References [1 [ G. Nardulli and G. Preparata, Phys. Lett. 117B (1982) 445. [21 N. Lockyer ctal., Phys. Rev. Lctt. 45 (1980) 1821. [3] G. NarduUi and G. Preparata, Phys. Lett. 104B (19811 399; G. Nardulli, G. Prcparata and D. Rotondi, preprint BA-GT 82/11, to be published in Phys. Rev. D.
332
17 March 1983
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