On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions
The reliability of the phenomenological estimates for the D⁺(1232) mass is questioned coming from the of π⁺ and π⁰ mesons photoproduction data off proton target till the end of 2001. The origin of an old discrepancy for the D⁺(1232) mass presented in tables of the Particle Data Group is discussed....
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Cite this: | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions / A.S. Omelaenko // Вопросы атомной науки и техники. — 2002. — № 2. — С. 3-6. — Бібліогр.: 17 назв. — англ. |
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| citation_txt | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions / A.S. Omelaenko // Вопросы атомной науки и техники. — 2002. — № 2. — С. 3-6. — Бібліогр.: 17 назв. — англ. |
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| description | The reliability of the phenomenological estimates for the D⁺(1232) mass is questioned coming from the of π⁺ and π⁰ mesons photoproduction data off proton target till the end of 2001. The origin of an old discrepancy for the D⁺(1232) mass presented in tables of the Particle Data Group is discussed.
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N U C L E A R R E A C T I O N S
ON THE EXPERIMENTAL VALUE OF THE ∆+(1232) MASS
FROM γp→nπ+(pπ0) REACTIONS
A.S. Omelaenko
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
The reliability of the phenomenological estimates for the ∆+(1232) mass is questioned coming from the of π+ and
π0 mesons photoproduction data off proton target till the end of 2001. The origin of an old discrepancy for the ∆
+(1232) mass presented in tables of the Particle Data Group is discussed.
PACS: 13.75Gx
1. INTRODUCTION
Up to present time the single pion photoproduction
reactions are the only source of information about the
parameters of the ∆+(1232) resonance [1]. This
information was obtained from the resonance fitting of
the resonant multipoles leading to the final πN state
with isotopic spin T=3/2 and total momentum J=3/2 that
are obtained in several energy independent analyses at
condition that Watson’s theorem is not used in treating
these multipoles. During the last decades the most
striking point here was the significant disagreement
between the ∆+(1232) mass 1234.9±1.4 MeV obtained
by authors of work [2] using the results of their
preceding energy independent analysis with “free”
imaginary part of the magnetic dipole resonant
amplitude [3], and other papers cited in [1]. In
particular, this value is considered as inconsistent with
∆0 and ∆++ masses, 1233.6±0.5 MeV and 1230.9±
0.3 MeV respectively found in more recent pion
nucleon analyses [4].
It should be noted that ∆0 and ∆++ masses are defined
as energy at which the corresponding πN phase shifts
are crossing the value π/2, or, equivalently, the real
parts of the resonant partial waves equal zero (the
“experimental observed” values). They can be found,
for example, by fitting the P33 amplitudes with using the
Breit-Wigner resonance formulas. Of course, one can
try to get more underlying resonance parameters by
separating the amplitude into the “proper resonance”
and a background. Such problem is rather complicated
and model dependent. The masses obtained in this way
have different physical meaning. Usually they are very
different from the values mentioned above (for example,
1241 MeV [5], 1251.1 МeV [6], 1235.1 МeV and
1256.0 МeV [7]). In general there is the whole
hierarchy of mass and width parameters describing the
∆(1232) isobar: a) the “experimental” values we have
just discussed refer to the “dressed” resonance with
unitary addition of the background; b) parameters of the
resonance, dressed by independently introduced
background; c) parameters of the “pure” resonance
propagating in the absence of any background; d) mass
of the “bare” resonance possessing zero width (relevant
calculations in the framework of a nonrelativistic model
[8,9]can be found in [10]). It is clear that one can
discuss some effect of the isotopic splitting only
comparing the parameters corresponding to the same
level of the dynamical description. In particular the
mentioned before ∆+ mass has to be searched as the
energy at which the real parts of the resonant multipoles
pass through zero.
Here we estimate the role of different factors at
determination of the “experimental” ∆+(1232)
parameters by direct fitting the modern photoproduction
data. In this calculations the resonance parameters were
determined as ones of the Walker’s formula [11]
invoked to describe the resonant multipole amplitudes,
with a little generalization introduced to test the energy
excitation function.
2. THE RESONANCE MODEL
OF THE ∆+(1232) PHOTOEXCITATION
In the first resonance region the real parts of the
background single pion photoproduction multipoles
were taken as the Born approximation completed in s-,
p- and d-multipoles by the following cubic polynomials
(indexes + and − correspond to the total angular
momenta j=l±1/2):
=γ± )(Re EM I
l
.)()()(
4
)(
1
)()()()(
4
1
Re ∏∑
=
≠
=
γγλγλ
=
=
± −−
j
ij
j
jiji
i
i
I
l EEEEEM
(1)
Here BAM I
l
I
l
I
l ±±± ≡ , are defined according to [11]
spiral multipoles with following isospin structure
A1/2 = 1/3 A(π0) + √2/3 A(π+),
A3/2 = A(π0) − 1/√2 A(π+).
Index l is the orbital angular momentum, E i)(
γ is a knot
value of the current photon energy Eγ. Taking the Р33 πN
scattering partial amplitudes to be purely elastic
imaginary parts of the spiral background multipoles up
to l=3 were calculated according the Watson’s theorem
with using the phase shifts .)(2,2δ ±lI from the πN elastic
scattering analyses:
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2002, № 2.
Series: Nuclear Physics Investigations (40), p. 3-6. 3
).(ReIm )(2,2δ= ±±± lI
I
l
I
l tgMM (2)
The resonant multipole amplitudes A 2/3
1+ and B 2/3
1+
were written using the Walker’s formula for
contribution of the ∆(1232) resonance:
.)(Im
)(
0
22
0
000
0
2/3
1
2/3
1
Γ−−
ΓΓ
=
+
+
π
γπ
WiWW
W
kq
qkWMC
WM
M (3)
Here W and W0 are the total c. m. energy and its value at
resonance, respectively, CM≡ )(Im 0
2/3
1 WM + is the
resonance constant. The energy dependent widths were
parameterized with introduction two phenomenological
parameters Xπ, Xγ:
,)(
22
22
0
0
2
0
−
−
ΓΓ =
Xk
Xk
k
k
g
W
γ
γ
γ (4)
.)(
22
22
0
0
3
0
−
−
ΓΓ =
Xq
Xq
q
q
W
π
π
π (5)
In Eqs. (4)-(5) k, q are the c. m. momenta of the photon
and pion, respectively, k0, q0 being the corresponding
quantities at W0. The parameter g is controlling the
energy dependence of the resonant multipoles via ratio
k/ko: at g=0.5 such a contribution in energy dependence
is absent at all, at g=1 and Xπ = Xγ≡ X the Walker’s
formula for ∆(1232) is reproduced, and g=1 corresponds
to the kq factor appearing in the resonant multipoles in
the Born approximation.
In our approach this resonance mechanism
represents the whole resonant multipoles without any
additional background contributions. Accordingly,
parameters M0 and Γ0 are the “experimentally observed”
mass and width discussed in Introduction.
3. NUMERICAL CALCULATIONS
The calculations were fulfilled for several variants
involving one at a time a change in different factors
concerning the model used or modification in the load
of the experimental data to compare results with some
looking to be realistic standard variant. The initial
experimental information on pion photoproduction on
proton was taken from compilation [12] up December
2001 in photon energy interval from 280 MeV to
400 MeV (differential cross section and polarization
data). The energy knots 280, 320, 360, and 400 MeV in
Eq. (1) were introduced for the real parts of the
background multipoles. At calculating the imaginary
parts of the multipoles via Eq. (2) the πN phase shifts
from the Arndt’s analysis [13] were used.
In Table 1 the χ2 value per number of degree of
freedom Ndf, values of the resonance mass and width
obtained are presented at level with the corresponding
ratio EMR of the electrical quadrupole and the magnetic
dipole amplitudes at resonance. We used this ratio as
some additional criterion for quality estimation of our
solutions.
For the standard variant (the first line in Table 1) the
resonance quantities at the level with the knot values of
the real parts of background multipoles A0+, A1+, A1-, A2-,
B1+, B2- with isotopic I=1/2, and A0+, A1- for T=3/2 were
determined by minimization of standard χ2 without
introducing rating factors for any type of observable.
All other multipoles were taken into account in
electrical Born approximation being unitarized up to the
partial waves with orbital momentum l=3. Parameter X
was fixed at the Walker’s value 185 MeV, and g=1. We
had to ignore the data provided by some experiments
with χ2/Ndf significantly exceeding 9.0. These are
mentioned in Table 2 in terms of the labels from
compilation [12] with addition of two letters from the
name of the laboratory. Accordingly, we used 3124
experimental points in this run.
Each subsequent line in Table 1 presents a run
involving some change in the data or modification in the
background or in the resonance description. The concise
clarification is presented in the relevant comment. Some
additional remarks are given below.
Line 1.The experimental ∆+ mass for the variant
practically coincides with the ∆0 mass.
Line 2.Restoration of the “bad” data increased χ2/Ndf,
with a small change of the ∆+ width only.
Line 3.In the s-, p-wave variant the ∆+ mass is situated in
the middle of the interval (∆++, ∆o). Besides, the
large value of theEMR ratio is coming close to the
upper values for E2/M1 cited in [1].
Line 4.Involving in fitting all background d-waves
makes ∆+ mass smaller. Large number of iterations.
Line 5.Introducing of the full Born approximation
makes our fit worse with significant enlargement of
the mass.
Line 6.The data before 1967 allow determination neither
the ∆+ mass nor the width.
Line 7.The database available at time of work [3].
Line 8. At this time the Kharkov experiments in the first
resonance region have already been done. The best-
looking result for the mass splitting. The ratio EMR
(≅ − 1.5%) is close to the E2/M1 for this years
[1,14].
Line 9.X= 300.30 ± 15.11, significant correlations,
many iterations. Weak dependence on X.
Line 10.Xγ =185 MeV, free parameter Xπ goes to ∞.
Line 11.Xπ=185 MeV, free parameter Xγ goes to zero
and is strongly correlated.
Line 12.Introducing the kq dependence of the resonance
multipoles gives unreasonably small mass.
Line 13.Relaxation of the resonance energy dependence
via ratio k/ko gives too large mass.
Line 14.Variant with taking into account the true π0
mass in the q factor for cross section and in the
resonance contribution at π0 production. The mass
shift is three times greater then statistical error.
Line 15.Cross section data of some laboratories have
been multiplied by the normalization factors Nlab
being defined from the fit simultaneously with other
parameters of the standard run (results for Nlab are
given in Table 3). The correlation factors for Nlab are
close to 1 and do not exceed 1.2. A significant
decrease of the χ2/Ndf is observed; the answer for the
∆+ mass is practically the same as in the standard run
4
(to compare with effect of the normalization
procedure in the recent work [15]).
Table 1. ∆+ “experimental” parameters for different variants of the resonance model
№ Comment χ2/Ndf M0, MeV Γ0, MeV EMR, %
1 Standard 3.1176 1233.46 ± .15 116.26 ± .64 -2.07 ± .05
2 All data 3.8424 1233.39 ± .15 114.59 ± .59 -2.14 ± .05
3 s-, p-waves 3.6635 1232.31 ± .13 130.50 ± .53 -3.36 ± .05
4 s-, p-, d-waves 2.3768 1231.09 ± .28 121.66 ± 1.04 -3.75 ± .06
5 Full Born 3.0392 1234.57 ± .14 122.01 ± 0.65 -2.30 ± .06
6 Data before 1967 1.2836 1255.2 ± 48.4 201.51 ± 255.1 4.29 ± 7.37
7 Data before 1977 2.5019 1233.78 ± .29 111.02 ± 1.07 -.60 ± .10
8 Data before 1984 2.8545 1232.71 ± .22 119.28 ± .90 -1.43 ± .08
9 Free X = Xπ =Xγ 3.0837 1233.59 ± .16 123.86 ± .96 -2.06 ± .06
1
0
Free X = Xπ 2.8429 1242.63 ± .28 155.80 ± 1.37 -2.80 ± .08
1
1
Free X= Xγ 3.0180 1237.33 ± .35 116.92 ± .71 -2.31 ± .09
1
2
g=3/2 3.5209 1227.18 ± .11 109.38 ± .51 -1.95 ± .05
1
3
g=1/2 2.9686 1239.36 ± .20 120.05 ± .76 -2.42 ± .07
1
4
Corrected π0 mass 3.1371 1234.06 ± .15 118.09 ± .66 -2.13 ± .06
1
5
Normalization 2.7476 1233.43 ± .15 116.84 ± .64 -2.08 ± .06
Table 2. The data removed from the database
Reaction Observable Data Npnt
Energy interval,
MeV
Angle interval,
deg. χ2/Npnt
γp→nπ+ dσ/dΩ BL01LE 32 286 322 20.0 170.0 29.2
dσ/dΩ KN63UC 11 290 290 .0 160.0 16.0
Sigma LU64ST 3 330 330 45.0 135.0 27.4
Sigma ZD72ST 1 390 390 135.0 135.0 22.5
γp→pπ0 dσ/dΩ HA97MA 43 283 379 10.0 170.0 19.0
dσ/dΩ BL01LE 35 286 334 70.0 130.0 12.8
dσ/dΩ HE73TO 2 350 400 6.0 6.1 9.1
Table 3. The cross section data normalized on
factors Nlab
Reaction Data Nlab
γp→nπ+ FU77TO 0.9172 ± .0040
AV66ST 0.9424 ± .0189
AL63BO 0.9296 ± .0089
BU94BO 0.9948 ± .0054
AK71LE 1.0566 ± .0146
DU80BO 0.9298 ± .0058
DA01BO 0.9557 ± .0060
FR63BO 1.0721 ± .0173
BT68OR 1.0433 ± .0045
γp→pπ0 BW71BO 1.0395 ± .0049
MO69OR 1.1051 ± .0103
DO76LU 0.9253 ± .0086
DO77LU 0.9448 ± .0156
AK78LE 1.0673 ± .0073
HR74BO 0.9493 ± .0060
DO75LU 0.9499 ± .0257
BC67FR 0.9572 ± .0708
BC73BO 0.8835 ± .0646
4. DISCUSSION
Of coarse, the use of the resonance model for
determination of the ∆+(1232) mass is a constrained
method in comparison with the energy independent
analysis without Watson’s theorem for resonant
multipoles. Nevertheless in the latter case one has to use
some resonance model to get the resonance parameters,
too. So, direct application of the resonance model is the
simplest way to take into account correlation of the
resonance parameters with the initial experimental data.
5
The smooth parameterization of multipoles achieved
instead of histogram description with some arbitrary
energy bins can be treated as an additional advantage.
Concerning the result of results submitted in [2] we
would like to mention that the resonance parameters in
this work do not apply to the experimentally
“measured” ones, as ∆0 and ∆++ parameters in πN
scattering, but actually refers to the problem of explicit
separation of the resonance and the background. To
describe the resonant magnetic dipole amplitude M(3/2)
1+
the authors of [2] invoked the Olsson’s Eq. (8) [16] (but
with usual addition of the resonance and background
phase shifts for the elastic reaction. In [16] the
corresponding algorithm has another form, which is
roughly subtraction instead of summation.). The
Olsson’s receipt does not agree with the relevant
formula from the Noille’s unitary approach [17]. From
physical point of view the latter one seems to be more
convincing. However, the important point is that in both
approaches the Watson’s theorem is treated as
underlying property. So, it is principally inadequate to
use them to analyze the resonant multipole obtained
with refusal of the Watson’s theorem. Certainly, one can
treat such a formula as some empirical parameterization.
But in this case one has to determine the experimental ∆
+ mass as the energy point at which the real part of
resonant multipole passes through zero. In analysis [3],
which allowed releasing from the Watson’s theorem for the
T=3/2 magnetic dipole amplitude only, this occurs for the
photon energy near 350 MeV. So, the experimental mass
would even exceed 1234.9 MeV. It looks quite natural
keeping in mind the experimental database before 1977 (at
that time, for example, the main polarization experiments of
Kharkov were yet not fulfilled). Nevertheless, our relevant
retrospective run (line 7 in Table 1) has given the ∆+ mass
1233.78 ± .29 MeV looking more acceptable.
5. CONCLUSIONS
In the region of excitation of the first nucleon
resonance the photoproduction on proton allows good
determination of the main s-, p-wave partial amplitudes
of pion photoproduction on proton target with taking
into account d-wave correction, too. Stable
determination of the ∆+(1232) mass and width can be
treated as an encouraging moment. In spite of the
simplest form used to describe the resonant multipoles
the value EMR occurred to be close to the E2/M1 ratio
defined with using the Watson’s theorem (usually in the
Noelle’s approach). But there are many factors that have
significant influence on the experimental mass and
width values of the ∆+ resonance. This is the problem of
selection and possible normalization of the data used,
and different possibilities concerning the background
and description of the resonance contribution in the
amplitude. The mass in several cases occurred to be
beyond the interval restricted by ∆0 and ∆++ masses.
Nevertheless that is not the case for variants looking the
most reliable from the point of view of reasonable
balance between the existing data and the amount of the
parameters to define from the fits. It is interesting to
remark that between tested modifications of the Breit-
Wigner formula one used by Walker occurred to be the
most adequate.
Comparison fits with the data restricted by different
years shows that the new data are entailing the evident
shift of the ∆+ mass value. As modern data about some
single polarization observables are yet absent a new
precise experiments in the reaction of pion
photoproduction on proton are extremely desirable.
On the other side, the results of the calculation show
that the phenomenological treatment of the present-day
photoproduction database for the ∆(1232) excitation
region needs the formalism taking into account
difference of π+ and π0 masses.
ACKNOWLEGMENT
The author would like to thank I.I. Strakovsky for
kindly sending the information about article [14].
REFERENCES
1. D.E. Groom at al. (Particle Data Group) //
Eur. Phys. J. 2000, v. C15, p. 1 (and 2001 particle
update for edition 2002, URL:http://pdg.lbl.gov).
2. I.I. Miroshnichenko, V.I. Nikiforov, V.M. Sanin,
P.V. Sorokin, and S.V. Shalatsky. Position and residue
of the pole in the M(3/2)
1+
amplitude of the reaction γp→
Nπ // Yad. Fiz. 1979, v. 29, p. 188-193 [Sov. J. Nucl.
Phys. 1979, v. 29, p. 94-99].
3. I.I. Miroshnichenko, V.I. Nikiforov, V.M. Sanin,
P.V. Sorokin, and S.V. Shalatsky. Multipole analysis of
single pion photoproduction in region of the P33
resonance // Yad. Fiz. 1977, v. 26, p. 99-108.
4. R. Workman. Remarks on the ∆+(1232) mass //
Phys. Rev. 1997, v. C56, p. 1645-1646.
5. R. Cenni, G. Dillon, P. Christillin. Dynamical
model for π-photoproduction in the ∆-channel // Nuovo
Comento. 1987, v. 97A, p. 9-23.
6. R.M. Davidson, N.C. Mukhopadhyay,
R.S. Wittman. Effective-Lagrangian approach to the
theory of pion photoproduction in the ∆(1232) region //
Phys. Rev. D. 1991, v. 43, p. 72-94.
7. A.S. Omelaenko. Determination of the parameters
of the ∆(1232) resonance from the partial-wave analyses
of elastic πN scattering // Yadernaya. Fizika. 2002,
v. 65, p. 566-572 [Physics of Atomic Nuclei. 2000,
v. 65, p. 539-545].
8. N. Tanabe, K. Ohta. Dynamical model for pion
photoproduction in the ∆ region // Phys. Rev. C. 1985,
v. 31, p. 1876-1884.
9. S. Nozawa, B. Blankleider, T.-S.H. Lee. A
dynamical model of pion photoproduction on the
nucleon // Nucl. Phys. A. 1990, v. 513, p. 459-510.
10. A.S. Omelaenko. Determination of the mass and
width of the ∆(1232) resonance within the framework of
a nonrelativistic model with a separable potential //
Ukrainian Physical Journal. 1996, v. 41, p. 524-529.
11. R.L. Walker. Phenomenological analysis of
single-pion photoproduction // Phys. Rev. 1969, v. 182,
p. 1729-1748.
6
12. The George Washington University, Center for
Nuclear Studies, Data Analysis Center.
http://gwdac.phys.gwu.edu
13. A. Arndt, R.L. Workman, I.I. Strakovsky,
M. Pavan. Partial-wave analysis of πN-scattering.
Eprint nucl-th/9807087 (submitted to Phys.
Rev. C).
14. A.S. Omelaenko, P.V. Sorokin. Ratio of the
quadrupole and dipole ∆→Nγ transition amplitudes
from multipole analysis of the raction γp→nπ+(pπ0) //
Yadernaya Fizika. 1983, v. 38, p. 668-673 [Sov. J. Nucl.
Phys. 1983, v. 38, p. 398-403].
15. A.A. Arndt, W.J. Briscoe, I.I. Strakovsky,
R.L. Workman. Analysis of pion photoproduction data
// Phys. Rev. C. 2002 (to be published); eprint nucl-
th/0205067, 33 p.
16. M.G. Olsson. Does the ∆(3,3) resonance
factorize? // Phys. Rev. D. 1976, v. 13, p. 2502-2507.
17. P. Noelle. Baryon Resonances and Electro-
magnetic Couplings // Prog. Theor. Phys. 1978,
v. 60, p. 778-793.
7
|
| id | nasplib_isofts_kiev_ua-123456789-80101 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:54:31Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Omelaenko, A.S. 2015-04-11T19:05:45Z 2015-04-11T19:05:45Z 2002 On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions / A.S. Omelaenko // Вопросы атомной науки и техники. — 2002. — № 2. — С. 3-6. — Бібліогр.: 17 назв. — англ. 1562-6016 PACS: 13.75Gx https://nasplib.isofts.kiev.ua/handle/123456789/80101 The reliability of the phenomenological estimates for the D⁺(1232) mass is questioned coming from the of π⁺ and π⁰ mesons photoproduction data off proton target till the end of 2001. The origin of an old discrepancy for the D⁺(1232) mass presented in tables of the Particle Data Group is discussed. The author would like to thank I.I. Strakovsky for kindly sending the information about article [14]. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Nuclear reactions On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions О величине экспериментального значения массы ∆⁺ (1232) резонанса из реакций γp→nπ⁺ (pπ⁰) Article published earlier |
| spellingShingle | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions Omelaenko, A.S. Nuclear reactions |
| title | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions |
| title_alt | О величине экспериментального значения массы ∆⁺ (1232) резонанса из реакций γp→nπ⁺ (pπ⁰) |
| title_full | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions |
| title_fullStr | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions |
| title_full_unstemmed | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions |
| title_short | On the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions |
| title_sort | on the experimental value of the ∆⁺ (1232) mass from γp→nπ⁺ (pπ⁰ ) reactions |
| topic | Nuclear reactions |
| topic_facet | Nuclear reactions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/80101 |
| work_keys_str_mv | AT omelaenkoas ontheexperimentalvalueofthe1232massfromγpnπpπ0reactions AT omelaenkoas oveličineéksperimentalʹnogoznačeniâmassy1232rezonansaizreakciiγpnπpπ0 |