Negative pion photoproduction off polarized deuteron target
It is discussed whether the target asymmetry (TA) for γn→π⁻p can be extracted from data on γd→π⁻pp. An exclusive experiment that enhances production of pions on neutron at rest and suppresses contributions of the recoil mechanism is shown to correspond to this purpose. The relation between the TAs f...
Gespeichert in:
| Veröffentlicht in: | Вопросы атомной науки и техники |
|---|---|
| Datum: | 2002 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/80104 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Negative pion photoproduction off polarized deuteron target / A.A. Belyaev, A.V. Kotlyar, A.A. Lukhanin, P.V. Sorokin // Вопросы атомной науки и техники. — 2002. — № 2. — С. 16-18. — Бібліогр.: 17 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-80104 |
|---|---|
| record_format |
dspace |
| spelling |
Belyaev, A.A. Kotlyar, A.V. Lukhanin, A.A. Sorokin, P.V. 2015-04-11T19:16:47Z 2015-04-11T19:16:47Z 2002 Negative pion photoproduction off polarized deuteron target / A.A. Belyaev, A.V. Kotlyar, A.A. Lukhanin, P.V. Sorokin // Вопросы атомной науки и техники. — 2002. — № 2. — С. 16-18. — Бібліогр.: 17 назв. — англ. 1562-6016 PACS: 13.60.Le, 25.20.Lj https://nasplib.isofts.kiev.ua/handle/123456789/80104 It is discussed whether the target asymmetry (TA) for γn→π⁻p can be extracted from data on γd→π⁻pp. An exclusive experiment that enhances production of pions on neutron at rest and suppresses contributions of the recoil mechanism is shown to correspond to this purpose. The relation between the TAs for the reactions on deuteron and neutron is established taking into account pion and active nucleon rescattering in the final state and neglecting effects due to interaction with the spectator nucleon. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Nuclear reactions Negative pion photoproduction off polarized deuteron target Фоторождение отрицательных пионов на поляризованной дейтронной мишени Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Negative pion photoproduction off polarized deuteron target |
| spellingShingle |
Negative pion photoproduction off polarized deuteron target Belyaev, A.A. Kotlyar, A.V. Lukhanin, A.A. Sorokin, P.V. Nuclear reactions |
| title_short |
Negative pion photoproduction off polarized deuteron target |
| title_full |
Negative pion photoproduction off polarized deuteron target |
| title_fullStr |
Negative pion photoproduction off polarized deuteron target |
| title_full_unstemmed |
Negative pion photoproduction off polarized deuteron target |
| title_sort |
negative pion photoproduction off polarized deuteron target |
| author |
Belyaev, A.A. Kotlyar, A.V. Lukhanin, A.A. Sorokin, P.V. |
| author_facet |
Belyaev, A.A. Kotlyar, A.V. Lukhanin, A.A. Sorokin, P.V. |
| topic |
Nuclear reactions |
| topic_facet |
Nuclear reactions |
| publishDate |
2002 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Фоторождение отрицательных пионов на поляризованной дейтронной мишени |
| description |
It is discussed whether the target asymmetry (TA) for γn→π⁻p can be extracted from data on γd→π⁻pp. An exclusive experiment that enhances production of pions on neutron at rest and suppresses contributions of the recoil mechanism is shown to correspond to this purpose. The relation between the TAs for the reactions on deuteron and neutron is established taking into account pion and active nucleon rescattering in the final state and neglecting effects due to interaction with the spectator nucleon.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/80104 |
| citation_txt |
Negative pion photoproduction off polarized deuteron target / A.A. Belyaev, A.V. Kotlyar, A.A. Lukhanin, P.V. Sorokin // Вопросы атомной науки и техники. — 2002. — № 2. — С. 16-18. — Бібліогр.: 17 назв. — англ. |
| work_keys_str_mv |
AT belyaevaa negativepionphotoproductionoffpolarizeddeuterontarget AT kotlyarav negativepionphotoproductionoffpolarizeddeuterontarget AT lukhaninaa negativepionphotoproductionoffpolarizeddeuterontarget AT sorokinpv negativepionphotoproductionoffpolarizeddeuterontarget AT belyaevaa fotoroždenieotricatelʹnyhpionovnapolârizovannoideitronnoimišeni AT kotlyarav fotoroždenieotricatelʹnyhpionovnapolârizovannoideitronnoimišeni AT lukhaninaa fotoroždenieotricatelʹnyhpionovnapolârizovannoideitronnoimišeni AT sorokinpv fotoroždenieotricatelʹnyhpionovnapolârizovannoideitronnoimišeni |
| first_indexed |
2025-11-24T03:45:52Z |
| last_indexed |
2025-11-24T03:45:52Z |
| _version_ |
1850427095112482816 |
| fulltext |
NEGATIVE PION PHOTOPRODUCTION
OFF POLARIZED DEUTERON TARGET
A.A. Belyaev 1, A.V. Kotlyar 2, A.A. Lukhanin 1, P.V. Sorokin 1
1 National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
e-mail: belyaev@kipt.kharkov.ua
2 Kharkov National University, 61077 Kharkov, Ukraine
It is discussed whether the target asymmetry (TA) for pn _πγ →
can be extracted from data on ppd _πγ →
. An
exclusive experiment that enhances production of pions on neutron at rest and suppresses contributions of the recoil
mechanism is shown to correspond to this purpose. The relation between the TAs for the reactions on deuteron and
neutron is established taking into account pion and active nucleon rescattering in the final state and neglecting effects
due to interaction with the spectator nucleon.
PACS: 13.60.LE, 25.20.LJ
The attention paid to the process ppd _πγ → springs to
some extent from the hope to obtain observables for
pn _πγ → in the absence of a neutron target and to acquire
information on the elementary neutron amplitude. Thus,
for example, it was shown [1] that the differential cross
sections of the quasifree exclusive reaction and the pro-
cess off nucleon are proportional in the framework of
the spectator model up to the plane-wave
approximation. So, the reaction on deuteron under certain
kinematic conditions can be useful for exploring the
properties of the elementary operator for pion
photoproduction.
As known, studies of the polarization phenomena
can bring detailed information about different aspects of
the reaction mechanisms. Influence of small amplitudes
on spin observables is enhanced providing possibility to
investigate subtle dynamical effects. The TA in photo-
production of negative pions off polarized deuteron was
measured in experiments [2-4] covering the energy
range from 0.280 GeV to 2 GeV. Data analysis in
articles [2-4] has been carried out with the help of a pro-
cedure that introduces polarization of active nucleon. In
its turn, this quantity is determined by the deuteron D-
state probability and is model dependent.
In the present article we attempt to establish an rela-
tion between TAs in the reaction on deuteron and one for
the process on free neutron, elucidate necessary assump-
tions and to determine kinematic conditions favorable for
reduction of the various corrections violating the relation.
To describe the polarized deuteron target the forma-
lism of density matrix is commonly used. The density
matrix for deuteron in magnetic field collinear to the y-
axis can be written as [5,6]
),ˆˆ1(ˆ
2
1
2
3
3
1
yy
d
yyy
d
y
d pp ++=ρ (1)
where the Goldfarb operators yy Ŝˆ = and =yŷ
,ˆ2ˆ3 2 IS y −= the spin operator is Ŝ
, and Î is a unit 3�3-
matrix. Formally, the polarization parameters d
yp and
d
yyp are constrained [5,6] by the inequalities ≤≤− yp1
1 and .12 ≤≤− yyp
We use the right-handed coordinate system specified
as follows. The z-axis is taken along the photon momentum
,k
the y-axis is directed along the vector ,qk
× where q
is the momentum of the ejected pion. The reaction plane is
defined by the vectors k
and .q
The polarization and the alignment are −= )1(wpd
y
)1(−− w and ),0(31 wpd
yy −= where the spin level popu-
lations are denoted by )( dMw ( 1)( =∑
dM dMw ) with
dM being the projection of the deuteron total momentum
on the z-axis. On the supposition that the deuteron spin
system can be described by a single temperature dT , the
populations )( dMw at low temperature and for a large
magnetic field H take the form [7-10] of a Boltzmann
distribution )exp()1(/)0()0(/)1( α=−= wwww , where
,/ dd kTHµα = dµ is the deuteron magnetic moment,
k is the Boltzmann constant. One has
)1)1(0(),)0(1()1(
))0(0(,)ch21()0(
2
1
3
11
<±<±−=±
≤<+= −
wuww
ww α
where .))0(3)0(21( 2/12wwu −−±= Sign +(-) in the ex-
pression for u corresponds to the direction of the magne-
tic field parallel (antiparallel) to the y-axis.
In the framework of the model discussed, the polari-
zation parameters satisfy ,11 <<− d
yp 10 <≤ d
yyp and
.043 22 =−+ yyyyy ppp For instance, in Kharkov experi-
ment [3] 42.035.0 =d
yp and according to the model
.14.009.0 =d
yyp
16 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 16-18.
For the deuteron spin state described by the density
matrix (1) the cross section of ppd _πγ →
casts into the
form ),1(
2
1
2
3
0
d
yy
d
yy
d
y
d
y
dd TpTp ++= σσ where is the
cross section for the reaction with the unpolarized particles
†
3
1
0 Tr AARdd =σ , the vector and tensor TAs =d
y
dT0σ
†
3
1 ˆTr AAR y
d = and ,ˆTr †
3
1
0 AART yy
dd
yy
d =σ the
amplitude of the process is denoted by A . The explicit
form of the kinematic factor dR is determined by a choice
of the independent kinematic variables (see, e.g.,
[1,11,12]).
The vector asymmetry can be found from measurement
of the cross section )( d
y
d pσ with .dd
y pp ±= Really,
one has ).3/())()(( 0
ddddddd
y pppT σσσ −−= To get
the cross section d
0σ from the values of )( dd p±σ one
needs to know the tensor asymmetry d
yyT since
).)(2/())()((0
d
yy
dd
yy
ddddd Tpppp +−+= σσσ
On the other hand, the TA for the process on neutron
can be determined from the values of the cross section
)Tp(σ)(pσ n
y
n
y
nn
y
n += 10 with the neutron polarization
.nn
y pp ±= The observables are given by
.2/))()((
),2/())()((
0
0
nnnnn
nnnnnnn
y
pp
pppT
−+=
−−=
σσσ
σσσ
The TA can be calculated from ( ) ×=
− 1†Tr ffT n
y
,ˆTr †ff yσ× where σ
̂ is the Pauli vector in the spin
space of the nucleon. Note, that the photoproduction
operator f includes contributions arising from the
pion-proton rescattering.
The amplitude for ppd _πγ →
),,,;p,p()1(
),,;p,p(
23
32
λ
λλ
ds
s
dsMSM
MSMB
MSMBA
dS
−+
+=
(2)
can be expressed in terms of the same operator .f In
Eq. (2) the photon polarization is denoted by λ , the to-
tal spin (its projection) of the pair of protons is )( SMS ,
the momenta of the outgoing active and spectator pro-
tons are p2 and p3. The first (second) term in r.h.s of the
above equation corresponds to the direct (recoil) mecha-
nism of the reaction. The contribution of the direct me-
chanism is visualized in the figure below.
p
3
p
2p
n
q
p
d
k
Direct mechanism of ppd −→ πγ process. Effects of
rescattering on proton-spectator are not included. The
deuteron (neutron) momentum is pd (pn)
Neglecting interaction between the outgoing protons,
we take the antisymmetrized product of two plane waves
1))3,2(1(
1,;,
33222
1
32
==−=
===
Ts
Ts
MTSMpp
MTSMpp
for the final NN-system, where )3,2( is the transposition
of the space, spin and isospin coordinates of the protons
with numbers 2 and 3, )( TMT is the total isospin (its
projections) of the pair of protons.
We use the deuteron WF in the form
,)()()( 1
1∑=
L L
d
L
d
LM LpLM
M
MLM
M
M pnYCp ϕϕ
where ),( 322
1 kkp
−= ppnp
= , 2k and 3k are the
nucleon momenta, M is the projection of the deuteron
spin, )( pLϕ are the WF components with the orbital an-
gular momentum 2,0=L , and λ
βα
c
baC is the Clebsch-
Gordan coefficient.
For the amplitudes in the r.h.s. of Eq. (2) we have
.),2/(),;,( 332 ddsds MppfSMMSMppB
−= ϕλ λ
To find a relation between the TAs n
yT and d
yT we
consider the spherical components of the observables.
The expansion of the neutron and deuteron density mat-
rices )21(ˆ == Sn ρρ and )1(ˆ == Sd ρρ over the
spherical tensors (ST) can be written as
),(ˆ)()(ˆ STStS kk k κκ κρ ∑ ∗=
where [14] ,
2
1
1 ˆ)2/1(ˆ
κκ σ==ST κκ SST ˆ)1(ˆ
2
1
1 ==
and .ˆˆ)1(ˆ
'"'
2
1'12 MMMM MM SSCST ∑== κ
κ The cyclic com-
ponents of the spin operators are κσˆ and .ˆ
MS
The matrix elements of the ST are given by [14]
( ) .)12/()12()(ˆ' '
1
2/1 SM
SMk CSkSMSTSM κκ ++=
The ST [14] are related to ones defined in [5] as
.3ˆ)1(ˆ
κκ τ kk ST == Expression for the TAs [5] in
terms of ST [14] reads
( ) ††2/1 Tr )(ˆTr 12)( FFFSTFSST kk κκ += (3)
with F being the amplitude f or A for the reaction on
neutron or on deuteron. For the cartesian TA n
yT we have
)( 11112 +− += TTT in
y with ).2/1( == STT kκkκ In the
case of the process on deuteron the asymmetries are
202
1
22222
3
11113
)(
),(
TTTT
TTT
d
yy
id
y
−+−=
+=
+−
+−
with ).1( == STT kκkκ
Retaining only the S-wave component of the deute-
ron WF and the contribution of the direct mechanism we
get the spherical TAs for ppd _πγ →
in the form
,~)1()2/1(33)1(
2/12/1
1
2/1
1
κκ k
kk
k TkiST
−+== (4)
where
,||~ 2
"' "'
"'
"'
'2/1
"2/1 ∑∑ ∗= λ
λ
λ
λλ
κκ mm mm
mmm
mmmm
m
kmk fffCT (5)
17
,'2
1
2
1
' mfmf mm
λλ = and '',', mmm are the spin pro-
jections of the nucleon.
The TA for the process pn _πγ →
reads
.~3)2/1( κκ kk TiST == (6)
Eqs. (4) and (6) yield for the spherical components
(3) of the TAs
)21(23)1( 11 === STST κκ . (7)
For the cartesian components of the asymmetries we
get
.
3
2 n
y
d
y TT = (8)
Relations (7),(8 ) between the asymmetries have
been obtained without use of any particular form of the
operator f for the elementary process pn _πγ →
. At
the same time, one needs to assume that the relative role
of the off-energy-shell effects in photoproduction on
bound nucleon are not substantial.
Eqs. (7) and (8 ) are valid in the frame of reference
where both the deuteron and the neutron are at rest. The
respective kinematic conditions can be provided, e.g., in
an exclusive experiment when the pion and the active
proton are detected in coincidence.
Taking into account the angular momentum selection
rules in Eqs. (4) or (5) we obtain .0)1(2 ==ST κ This
property of the tensor asymmetry can be expected in the
calculation including only the S-waves. As it was poin-
ted out [14], the tensor asymmetry in the radiative captu-
re of polarized deuteron on protons tends to zero when
S-waves are retained in the nuclear WFs.
Thus, we arrive at the conclusion that
))),()(((
/))()((
ddddd
ddddn
y
ppp
ppT
−+
−−=
σσ
σσ
(9)
i.e., the TA of the process pn _πγ →
can be found from
the yields for the reaction ppd _πγ →
under the assump-
tions that the pion production off the active nucleon do-
minates, neither rescattering on proton-spectator nor the
two-body reaction mechanisms are essential, the deuteron
D-wave does not affect the observables. Eq. (9) can be
used for treatment of the data obtained in the experiment
providing kinematic conditions for pion production on
neutron at rest for the contributions of direct mechanism.
In this kinematics the deuteron D-wave does not affect
photoproduction on active nucleon since 0)0(2 ==pϕ .
Simple relation (7) between the observables is derived
under the assumption that one can neglect a part of the re-
scattering effects. Final state interaction can play an impor-
tant role [15-17] in pion production off deuteron. Cetainly,
the contributions of the rescattering on proton-spectator
as well as ones due to antisymmetrization of final pp-
state can make difficult extraction of the TA for elemen-
tary process on neutron from the data on ._ ppd πγ →
Role of the recoil mechanisms will be studied in
forthcoming paper using in calculations the photopro-
duction operator constructed on basis of SAID and
MAID multipole analyses.
REFERENCES
1. R. Schmidt, H. Arenhoevel, P. Wilhelm.
Quasifree photoproduction on the deuteron in the
∆ region // Z. Phys. A, 1996, v. 355, p. 421-426.
2. K.H. Althoff, H. Beckschulze, R. Conrad et
al. Photoproduction of Negative Pions on Polarized
Neutron Target In The Resonance Region // Nucl.
Phys. B. 1975, v. 96, №3, p. 497-508.
3. V.L. Agranovich, A.A. Belyaev,
V.A. Get’man et al. T- asymmetry investigation in
pn −→↑ πγ reaction on polarized deuteron target //
VANT, ser. Nucl. Phys. Investigations. 1989, v. 8.
№8, p. 5-7(in Russian).
4. H. Fujii, S. Hayashii, R. Iwata et al. Measure-
ment of polarized target asymmetry on pn _πγ →
around the second resonance region // Nucl. Phys.
B. 1981, v. 187, №53, p. 53-70.
5. G.G Ohlsen. Polarization transfer and spin
correlation experiments in nuclear physics // Rep.
Mod. Phys. 1972, v. 35, p. 717-801.
6. O.F. Nemets, A.M. Yasnogorodsky. Polariza-
tion researches in nuclear physics. Kiev: “Naukova
dumka”, 1980, 352 p. (in Russian).
7. A. Abraham. The Principles of Nuclear Mag-
netism. Oxford: “Clarendon Press’’, 1961, 599 p.
8. M. Borghini and K. Scheffler. A butanol pola-
rized deuteron target // Nucl. Instr. Meth. A. 1971,
v. 95, №1, p. 93-98.
9. W. Meyer, K.H. Althoff, V. Burkert et al.
Tensor polarization in irradiated ND3 // Nucl.
Instr. Meth. A. 1986, v. 244, №3, p. 574-576.
10. B. Boden, V. Burkert, G. Knop et al. Elastic
electron deuteron scattering on a tensor polarized
solid ND3 target // Z. Phys. C. 1991, v. 49, №2,
p. 175-185.
11. M.I. Levchuk, M. Schumacher,
F. Wissmann. The reaction npH ),( 02 πγ in the
threshold region // Nucl. Phys. A. 2000, v. 675,
p. 621-636
12. M.I. Levchuk, M. Schumacher,
F. Wissmann. The inclusive reaction NN),(d πγ
in the first resonance region // nucl-th/0011041,
2000, 22 p.
13. D.A. Varshalovich, A.N. Moskalev and
V.K. Khersonskii. Quantum theory of Angular
Momentum. M.: “Nauka’’, 1975, 439 p. (in
Russian).
14. J. Jourdan, M. Baumgartner, S. Burzynski et
al. dp
− radiative capture and the 3He D-state //
Nucl. Phys. A. 1986, v. 453, №2, p. 220-240.
15. A.V. Shebeko. Effects of final state
interaction in direct nuclear reactions at
intermediate energies/ M: “MIFI”, 1991, 56 p. (in
Russian).
16. A.Yu. Loginov, A.A. Sidorov,
V.N. Stibunov. Effect of rescattering on
polarization observables of the reaction
18
−→ πγ ppd in the delta-resonance region //
Yad. Fiz. 2000, v. 63, №3, p. 459-467 (in Russian).
17. L.G. Levchuk, A.V. Shebeko. Near
threshold electroproduction of positive pions on a
deuteron // Yad. Fiz. 1999, v. 62, №1, p. 263-271
(in Russian).
19
A.A. Belyaev 1, A.V. Kotlyar 2, A.A. Lukhanin 1, P.V. Sorokin 1
1 National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
PACS: 13.60.Le, 25.20.Lj
REFERENCES
|