Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung
Astrophysical simulation of natural abundance of p-nuclei needs knowledge of the enormous quality of photonuclear reaction rates which can be derived from the reaction integral yields. The applicability of the activation technique for getting relevant experimental information is shown by the example...
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irk-123456789-804922015-04-19T03:02:18Z Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung Semisalov, I. Skakun, Ye. Kasilov, V. Popov, V. Ядерно-физические методы и обработка данных Astrophysical simulation of natural abundance of p-nuclei needs knowledge of the enormous quality of photonuclear reaction rates which can be derived from the reaction integral yields. The applicability of the activation technique for getting relevant experimental information is shown by the examples of the (γ; n)-reactions running in the ⁹⁶Ru and ⁹⁸Ru p-nuclei the measurements of the integral yields of which have been performed using bremsstrahlung of the Kharkiv electron linear accelerator. The obtained data are compared to the statistical theory of nuclear reactions. Астрофизическое моделирование природной распространенности так называемых p-изотопов требует сведений о скоростях низкоэнергетичных (припороговых) фотоядерных реакций на огромном числе атомных ядер. На примере (γ; n)-реакций, вызываемых фотонами в ядрах p-изотопов ⁹⁶Ru и ⁹⁸Ru , продемонстрирована возможность получения соответствующей экспериментальной информации на пучке тормозного излучения харьковского линейного ускорителя электронов путем измерения интегральных выходов реакций. Полученные результаты сравниваются с предсказаниями статистической теории ядерных реакций. Астрофiзичне моделювання природної розповсюдженостi так званих p-iзотопiв потребує знань швидкостей низькоенергетичних (припорогових) фотоядерних реакцiй на величезнiй кiлькостi атомних ядер. На прикладi (γ; n)-реакцiй, спричиняємих гальмiвним випромiнюванням харкiвського лiнiйного прискорювача електронiв в ядрах p-iзотопiв ⁹⁶Ru та ⁹⁸Ru , продемонстровано можливiсть отримання вiдповiдної експериментальної iнформацiї шляхом вимiрювання iнтегральних виходiв реакцiй. Отриманi результати порiвнюються з передбаченнями статистичної теорiї ядерних реакцiй. 2014 Article Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung / I. Semisalov, Ye. Skakun, V. Kasilov, V. Popov // Вопросы атомной науки и техники. — 2014. — № 5. — С. 102-110. — Бібліогр.: 38 назв. — англ. 1562-6016 PACS: 26.30.-k, 25.20.-x, 27.60.+j, 29.30.-h, 24.60.Dr http://dspace.nbuv.gov.ua/handle/123456789/80492 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Ядерно-физические методы и обработка данных Ядерно-физические методы и обработка данных |
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Ядерно-физические методы и обработка данных Ядерно-физические методы и обработка данных Semisalov, I. Skakun, Ye. Kasilov, V. Popov, V. Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung Вопросы атомной науки и техники |
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Astrophysical simulation of natural abundance of p-nuclei needs knowledge of the enormous quality of photonuclear reaction rates which can be derived from the reaction integral yields. The applicability of the activation technique for getting relevant experimental information is shown by the examples of the (γ; n)-reactions running in the ⁹⁶Ru and ⁹⁸Ru p-nuclei the measurements of the integral yields of which have been performed using bremsstrahlung of the Kharkiv electron linear accelerator. The obtained data are compared to the statistical theory of nuclear reactions. |
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Semisalov, I. Skakun, Ye. Kasilov, V. Popov, V. |
| author_facet |
Semisalov, I. Skakun, Ye. Kasilov, V. Popov, V. |
| author_sort |
Semisalov, I. |
| title |
Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung |
| title_short |
Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung |
| title_full |
Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung |
| title_fullStr |
Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung |
| title_full_unstemmed |
Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung |
| title_sort |
activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2014 |
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Ядерно-физические методы и обработка данных |
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http://dspace.nbuv.gov.ua/handle/123456789/80492 |
| citation_txt |
Activation technique of astrophysical photonuclear reaction rate measurements using bremsstrahlung /
I. Semisalov, Ye. Skakun, V. Kasilov, V. Popov // Вопросы атомной науки и техники. — 2014. — № 5. — С. 102-110. — Бібліогр.: 38 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT semisalovi activationtechniqueofastrophysicalphotonuclearreactionratemeasurementsusingbremsstrahlung AT skakunye activationtechniqueofastrophysicalphotonuclearreactionratemeasurementsusingbremsstrahlung AT kasilovv activationtechniqueofastrophysicalphotonuclearreactionratemeasurementsusingbremsstrahlung AT popovv activationtechniqueofastrophysicalphotonuclearreactionratemeasurementsusingbremsstrahlung |
| first_indexed |
2025-07-06T04:30:17Z |
| last_indexed |
2025-07-06T04:30:17Z |
| _version_ |
1836870499103145984 |
| fulltext |
ACTIVATION TECHNIQUE OF ASTROPHYSICAL
PHOTONUCLEAR REACTION RATE MEASUREMENTS
USING BREMSSTRAHLUNG
I. Semisalov∗, Ye. Skakun, V. Kasilov, V. Popov
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received January 22, 2013)
Astrophysical simulation of natural abundance of p-nuclei needs knowledge of the enormous quality of photonuclear
reaction rates which can be derived from the reaction integral yields. The applicability of the activation technique
for getting relevant experimental information is shown by the examples of the (γ, n)-reactions running in the 96Ru
and 98Ru p-nuclei the measurements of the integral yields of which have been performed using bremsstrahlung of the
Kharkiv electron linear accelerator. The obtained data are compared to the statistical theory of nuclear reactions.
PACS: 26.30.-k, 25.20.-x, 27.60.+j, 29.30.-h, 24.60.Dr
1. INTRODUCTION
Investigations of photonuclear reaction cross sections
at the giant resonance region energies made a valu-
able contribution to understand nuclear interaction
and atomic nucleus structure features. In addition,
photonuclear reaction data are applied to many tech-
nological decisions and penetrated to different sci-
ences promoting their developments. One of the re-
markable fields of photonuclear reaction knowledge
applications is nuclear astrophysics problems among
which the detail understanding of scenarios of origin
of chemical elements and their isotopes is crucial to
explain the natural abundance.
It is currently established that naturally occurred
stable isotopes were mainly resulted from low energy
nuclear reactions induced by different particles. Pho-
tonuclear reactions play primary role at stellar nucle-
osynthesis of so called p-nuclei ([1] and therein).The
last term is used to designate the stable weak abun-
dant isotopes of middle and heavy mass region (be-
tween A = 74 and A = 196) which are located on the
proton-rich wing of the isobaric valley of stability
but blocked to be produced by the neutron capture
s (slow)- and/or r (rapid)-processes [2, 3], by which
the bulk of trans-iron isotopes were synthesized. The
scenario in which the p-nuclei are synthesized was pri-
marily named p-process that to underline importance
of proton capture processes for the production of
proton-rich nuclei. However since proton capture re-
actions required too high temperatures and large den-
sities of stellar medium, photonuclear reactions hap-
pening at temperatures 2 ≤ T9 ≤ 3 (T9 = T/109K)
are now considered to have the dominant impor-
tance for the p-nuclei production. So the sub-
scenario of the p-nuclei production by complete sub-
sequences of (γ, n), (γ, p) and (γ, α)-reactions was
named γ-process. The most suitable astrophysical
site for the γ-process is the deep oxygen-neon-rich
layers of massive stars exploding as type-II super-
nova [4, 5, 6].
Stellar simulation of the p-nuclei production re-
quires knowledge of the reaction rates of an enormous
network of reactions, a large part of which is pho-
todissociation interactions. Moreover, many of these
reactions occur on radioactive and excited nuclei of a
star interior and therefore cannot be measured under
terrestrial conditions. Thereupon theoretical calcu-
lations take on special importance. The statistical
model of Hauser-Feshbach (H-F) [7] is usually used
for this aim since low energy nuclear reactions run
through the stage of the compound nucleus forma-
tion. Several computer codes [8, 9, 10] implementing
the H-F theory are purposely tailored to calculations
of the astrophysical reaction cross sections and reac-
tion rates. These codes can by-turn be put to test
themselves by comparison with known experimental
data.
In recent years some groups performed mea-
surements of photonuclear reaction cross sec-
tions on series of middle and heavy nuclei at
stellar nucleosynthesis relevant energy region us-
ing bremsstrahlung [11, 12, 13, 14, 15] and
quasi-monoenergetic photons from Laser Compton
Backscattering (see [16, 17, 18] and review [19])
and analyzed them using the H-F model computer
codes [8, 9, 10, 20]. However, current databases
(cf. KADoNIS database [21]) show the scarce of
available data in question. A line of the p-type
isotopes are placed in the A = 90...100 mass number
region. The chains of the molybdenum (Mo), tech-
∗Corresponding author E-mail address: semisalovil@kipt.kharkov.ua
102 ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2014, N5 (93).
Series: Nuclear Physics Investigations (63), p.102-110.
netium (Tc), ruthenium (Ru), and rhodium (Rh)
isotopes and the ways of their star synthesis are
shown in Fig.1. The most of the natural molybde-
num (having masses 95 and more) and ruthenium
(masses 99 and more) isotopes were synthesized in
92 94 95 96 97 98 99
104
99
999896
100
100
100
101
101
101 102 103
103
rp p
p p s,r s,r s,r r
s,r s,r s,r
s,r
s
s
97 98
Mo
Tc
Ru
Rh
s process
r-process
104
97 104
r
93
p-process
Fig.1. (Color online) Chains of the molybdenum,
technetium, ruthenium, and rhodium isotopes and
the main nucleosynthesis processes producing them.
The light rectangles with solid and dashed boundaries
designate stable s- and/or r-nuclei and radioactive
ones, respectively. The orange rectangles designate
the 4 p-process nuclei of the molybdenum and
ruthenium isotopes
the s-process (the thick arrow line in Fig.1) and r-
process (the individual dashed blue arrows). However
both of these scenarios bypass the 92Mo, 94Mo, 96Ru,
and 98Ru isotopes (the shaded rectangles). These
last naturally occurring isotopes can not be formed
by s-process because of the 91Mo, 93Mo, 95Ru, and
97Ru isotope radioactivity and by r-process because
of the 92Zr, 94Zr, 96Mo, and 98Mo isotope stabil-
ity, respectively. A possible chance of these nuclei
creation is the p-process (The orange dashed arrows)
representing a combination of rapid proton capture
reactions (rp-process) and (γ, n), (γ, p) or (γ, α) pho-
tonuclear reactions (γ-process) on pre-existing s- and
r-nuclei as dominant way and the νp − process [4]
as an alternative one. So if the r-process widens the
valley of stability and the s-process elongates it to
heavier nuclei then the γ-process moves backward
from heavier nuclei to lighter ones.
In the present work we have attempted to adapt
the activation technique using bremsstrahlung of the
NSC KIPT electron linear accelerator (LINAC) and
high resolution gamma-ray spectrometry to study
photonuclear reactions in astrophysically relevant
energy region. We have measured the integral yields
of the (γ, n)-reactions on the 96Ru and 98Ru p-nuclei
at the near and above threshold energies and calcu-
lated their rates for the nucleus ground states. The
197Au(γ, n)196Au reaction was used as the standard
monitor reaction [22] and the 100Mo(γ, n)99Mo one
[15] to validate the experimental method.
2. FORMULATION OF STELLAR
PHOTONUCLEAR REACTIONS
The (γ, n)-reaction rate λ(T ) for a nucleus disposed
in a thermal photon bath of a stellar medium having
temperature T is defined by the expression [11]:
λ (T ) =
∫ ∞
0
cnγ (Eγ , T )σ(γ,n) (Eγ) dEγ , (1)
where c is the speed of light, σ(γ,n)(Eγ) the reaction
cross section depending on photon energy Eγ and the
number of photons nγ(Eγ , T ) per unit energy and
volume of a star interior is noticeably close to the
black-body or Planck distribution:
nγ (Eγ , T ) =
(
1
π
)2 (
1
h̄ c
)3 E2
γ
exp (Eγ/kT )− 1
, (2)
with the Boltzmann constant k.
The Planck distribution is illustrated by the dashed
curve (left ordinate axis) in Fig.2 for the stellar plasma
temperature T9 = 3 which is the relevant temperature of
the γ-process.
5 10 15
2
4
6
n
(E
,T
) [
10
29
M
eV
-1
cm
-2
]
Photon energy [MeV]
96Ru( ,n)95Ru
Planck
distribution
Gamow
window Cross
section
S
n
0,1
0,2
C
ro
ss
se
ct
io
n
[b
ar
n]
Fig.2. (Color online) Astrophysically relevant energy
range for the (γ, n)-reaction. The dashed black curve
(left ordinate axis) is the Planck distribution at T9 = 3
temperature, the dotted one (blue in color, right ordinate
axis) the excitation function of the 96Ru(γ, n)95Ru
reaction calculated with the NON-SMOKER code [9] of
the H-F statistical theory, the solid one (red in color,
relative units) the integrand of Eq. 1
The 96Ru(γ, n)95Ru reaction excitation function
calculated with the NON-SMOKER code [9] of the
H-F statistical model is shown by the dotted (blue in
color) curve (right ordinate axis). The integrand in Eq. 1
being the product of the steep decreasing and steep in-
creasing functions is represented as a solid curve (red
in color) with the sharp maximum at the top energy
Eγ = Sn + kT/2 where Sn is the neutron separation en-
ergy, i.e. the (γ, n)-reaction threshold. It is evidently
essential at only close and above threshold energy. This
peak called the Gamow window by analogy with charged
particle induced reactions [23] determines the energy re-
gion within of which the (γ, n)-reaction cross sections
should be known to derive the reaction rate.
Since there are difficulties concerning radiation
strength functions at low energies, the estimated
(γ, n)-reaction cross section near threshold can be derived
from the Wigner approximation [24]:
σ(γ,n) (Eγ) = σ0
(
Eγ − Sn
Sn
)l+1/2
, (3)
103
in which l is the emitted neutron angular momentum
(l = 0 for s-wave), σ0 the normalization coefficient which
can be learned from the measured activation yield of pho-
tonuclear reaction. The cross section σ(γ,n)(Eγ) obtained
in such a way can be used to draw the reaction rate.
The scientific group of the Nuclear Physics Institute
of the Darmstadt University (Germany) had proposed an
alternative method [11, 12] to obtain the photonuclear re-
action rate which does not depend on the reaction cross
section energy form and consists in approximation of the
Planck spectrum by several bremsstrahlung spectra hav-
ing different end-point energies E0,i at the near and above
reaction threshold region (within 1.5...2.0 MeV):
cnγ (Eγ , T ) ≈
∑
i
ai (T )Φγ (Eγ , E0,i) . (4)
Here ai(T ) is a set of the weighting coefficients ad-
justed for a given stellar environment temperature T ,
Φγ(Eγ , E0,i) the number of the bremsstrahlung pho-
tons per unit energy [keV ] and area [cm2] interval
during irradiation. The example for the superposi-
tion of the 6 bremsstrahlung spectra calculated by us-
ing the Schiff formula [25] for a thin tantalum con-
verter at the end-point energies 10.82, 11.12, 11.30,
11.50, 12.00, and 12.50 MeV (the 96Ru(γ, n)95Ru re-
action threshold equals 10.687 MeV) and multiplied by
respective values of the weighting coefficients ai(T ) ad-
justed for the Planck distribution at temperature T9 = 3
is shown in Fig.3. The alternating thin solid and dotted
curves imitate the above 6 Schiff bremsstrahlung spectra.
The result of their summing is presented by thick solid
(red in color) curve. The dashed (blue in color) line
is the Planck distribution. The superposition spec-
trum agrees with the Planck distribution at the high
energy bremsstrahlung fairly well. Disagreement be-
low the reaction threshold (the vertical arrow for the
96Ru(γ, n)95Ru reaction in Fig.3) does not matter.
10 12 14
1019
1021
1023
Superposition spectrum
Planck distribution (T=3.0 GK)
cn
(E
,T
) [
ke
V
-1
cm
-2
s-1
]
Bremsstrahlung end-point energy [MeV]
Sn
} Bremsstrahlung spectra
Fig.3. (Color online) Schiff spectra (alternating thin
solid and dotted curves) for the 6 end-point energies
(see text), the superposition spectrum (red solid thick
curve) for the 96Ru(γ, n)95Ru reaction and the Planck
distribution (blue dashed line) for T9 = 3 temperature.
The arrow Sn shows the reaction threshold
Substitution of the thermal Planck spectrum (Eq.4)
into Eq.1 gives Eq.5 connecting the reaction rate λ(T ) and
experimental activation yields Yi measured at the above
values of the bremsstrahlung end-point energies:
λ (T ) =
∑
i
ai (T )
∫ E0
Sn
σ(γ,n) (Eγ)Φγ (Eγ , E0,i) dEγ ∝
∑
i
ai (T )Yi. (5)
So to determine the photonuclear reaction rate
by the superposition method one needs to measure
the activation integral yields for six or more end-
point energies of the bremsstrahlung spectra within
the Gamow window range.
3. EXPERIMENTAL
The activation technique with the high resolution γ-
spectrometry based on the Ge(Li)-detector was ap-
plied for the measurements of the (γ, n)-reaction
yields on the 96Ru, 98Ru, and 100Mo nuclei. In
contrast to the direct counting of the emitted par-
ticle technique, the γ-spectrometry of the specified
radioactive residual nuclei makes possible to deter-
mine yields of individual reactions using target sam-
ples of the natural isotopic composition. Moreover,
in many cases simultaneous measurements of yields of
reactions occurring on different isotopes of the same
chemical element are possible. The latter circum-
stance is important at the experiments on weak abun-
dant p-nuclei.
3.1. ACCELERATOR OUTPUT AND
IRRADIATIONS
The intense bremsstrahlung flux was produced at the
Kharkiv LINAC, electron beam energy of which can
be varied from 6 to 30 MeV. Fig.4 illustrates the
scheme of our experimental setup for irradia-
tion of targets. The electron beam of about
20 µA average operating current was bent on an-
gle of 35◦ by a sector magnet (not shown in Fig-
ure) supplying 3% energy half-width. Having
passed through the 50µm titanium window the
beam hit in the 100µm tantalum converter which
was followed by the deflecting magnet to remove
any remaining electrons from the photon beam.
e-
e-
γ
Electron
beam Bremsstrahlung
Lead
shield
Ionization
chamber
Targets
8 mm lead
collimator
Beam
deflecting
magnet
100 μm tantalum
converter
Electron
accelerator
Fig.4. Sketch of the target irradiation at LINAC
The stemming Schiff distribution bremsstrahlung
was cut by the 8 mm lead collimator of the 100 mm
length mounted at the 400 mm distance downstream
the converter. Targets of interest elements of natural
isotopic composition stacked with the gold foil for the
104
standard 197Au(γ, n)196Au reaction were mounted in
the container which was positioned on the initial
electron beam axis immediately after the collimator.
The ruthenium targets of two types were used at
the experiments: (i) available thin (of ∼ 10mg/cm2
surface density) homogeneous self-supporting foils of
the 15 mm diameter made by the electro-deposition
technique [26] and (ii) the pressed pills of the high-
purity natural ruthenium metallic powder of the
m = (250...300) mg and ⊘ = 8 mm. In the case of
the last weight targets, irradiations were carried out
with no collimator. The high-purity metallic disks
of the 100 µm thickness were used as molybdenum
targets while the gold foils of the 20 mm diame-
ter and about 100 mg mass as the standard ones.
1 2 3 4 5 6 7
2000
4000
6000
C
ou
nt
s
Irradiation time [h]
Fig.5. Typical example of photon flux intensity on
a target during 7 hour irradiation monitored by the
ionization chamber
Maximum irradiation time (at low bremsstrahlung
end-point energies) reached 7 hours. The photon flux
was monitored by regular recording the X-ray dose
rate measured by the ionization chamber followed by
the target container and screened by the lead shield
from side background radiations. Fig.5 shows an ex-
ample of photon flux intensity as a function of time
during irradiation. The necessary corrections were
input at the reaction yield calculations in the cases
of essential photon flux fluctuations (see below).
3.2. Ge(Li)-DETECTOR
The integral yields of the (γ, n)-reactions under study
were determined by the activation equation (see be-
low) from the intensities of the γ-transitions fol-
lowing the β-decays of the produced long-lived ra-
dioactive nuclei. γ-Spectra were measured with
Ge(Li)-detector located in the low-background room
and surrounded with a thick lead shield. The mea-
surements of the absolute detector efficiency having
average uncertainty 5% were performed using 22Na,
60Co, 133Ba, 137Cs, 226Ra, and 241Am standard
sources. Energy dependences of the detector effi-
ciency for three source-to-detector distance are shown
in Fig.6.
The γ-spectrum of each irradiated target was
measured many times at different cooling times to
identify each peak by the γ-ray energy and half-life
of the residual. Distance between source and detec-
tor was chosen in this way that the dead time of the
acquisition system was not more than 4%. The er-
rors of detector efficiency, statistics, nucleus decay
scheme uncertainties and summing effects at high
count rate were taken into account at the calcula-
tions of the absolute number of the produced nuclei.
200 400 600 800 1000 1200 1400
10-3
10-2
10-1
r = 5 cm
r = 2 cm
Ef
fic
ie
nc
y
-ray energy [MeV]
r = 0 cm
Fig.6. (Color online) Energy dependence of ab-
solute efficiency of the Ge(Li)-detector for three
distances (r) ”source-detector”
3.3. DECAY FEATURES OF THE RESIDUAL
RADIOISOTOPES AND ACTIVITY
MEASUREMENTS
The decay schemes of the radioactive nu-
clei 95Ru and 97Ru produced in the stud-
ied 96Ru(γ, n)95Ru and 98Ru(γ, n)97Ru reac-
tions as well as 196Au and 99Mo as the prod-
ucts of the standard 197Au(γ, n)196Au and test
100Mo(γ, n)99Mo reactions are presented in Fig.7.
Fig.7. Simplified decay schemes of the 95Ru, 97Ru,
99Mo and 196Au residual radionuclides
Numerical data of the reaction thresholds, half-
lives, energies, and branching ratios of the ob-
served γ-transitions are given in Table. Fig.8
presents the examples of the γ-ray spectra emit-
ted by the Ru (upper panel), Mo (middle
panel), and Au (lower panel) targets irradiated
by the 13MeV end-point energy bremsstrahlung.
105
0
2000
4000
6000
0
2000
4000
6000
0 500 1000 1500
0
2000
4000
62
6
k
eV
95
R
u
33
6
k
eV
95
R
u
Ru target
E
brems
= 13.0 MeV
t
irr
= 6 h
t
cool
= 64 min
t
meas
= 1 h21
5
k
eV
97
R
u
0 1000 2000 3000 4000
Channel number
77
7
k
eV
73
4
k
eV
18
1
k
eV
C
ou
n
ts
/c
h
an
n
el 14
0
k
eV
35
5
k
eV
33
3
k
eV
-ray energy [keV]
Au target
E
brems
= 13.0 MeV
t
irr
= 6 h
t
cool
= 90 h
t
meas
= 1 h
Mo target
E
brems
= 13.0 MeV
t
irr
= 18 h
t
cool
= 266 h
t
meas
= 18 h
Fig.8. Decay γ−ray spectra of the ruthenium (upper
panel), molybdenum (middle panel) and gold (lower
panel) targets irradiated with the 13 MeV end-point
energy bremsstrahlung
The times of irradiation (tirr), cooling (tcool) and
measurement (tmeas) are shown in the panels. Each
peak of these spectra corresponds to full energy ab-
sorption of corresponding γ-rays following the decay
of one or another long-lived radioactive nucleus. Re-
action activation yields can be calculated from the
intensities of these peaks: for 95Ru formation via the
intensities of the γ-ray lines 336 and 626 keV, 97Ru
215 and 324 keV, 99Mo 140, 181, 739, and 777 keV
and 196Au 333 and 355 keV (see Table).
3.4. ACTIVATION YIELD CALCULATIONS
The experimental integral yield Yact(E0) of a
(γ, n)-reaction normalized to one target nucleus and
unit bremsstrahlung flux of end-point energy E0 is
determined from the intensity Nγ of the correspond-
ing γ-line via the conventional activation equation:
Yact (E0) =
Nγ
NtargλtirrεB
exp(λtcool)×
×{[1− exp(−λtirr)][1− exp(−λtmeas)]}−1 , (6)
in which Ntarg is the number of the target nuclei,
λ the radioactive decay constant, ε the detector ef-
ficiency, B the branching ratio of the observed γ-
transition, tirr, tcool and tmeas the times of irradia-
tion, cooling and measurement of the sample activity,
respectively. Eq.6 is correct in the case of constant
bremsstrahlung flux. If there are its remarkable fluc-
tuations during irradiation time we used the activa-
tion equation in the form:
Yact (E0) =
Nγ
NtargλtirrεB
{[1− exp(−λtmeas)]×
×
n∑
j=1
Ij
Itotal]
[1− exp(−λ∆tjirr)] exp(−λ∆tjcool)}
−1 , (7)
where
Ij
Itotal
is the ratio of number of counts of the
ionization chamber in j-th irradiation interval to the
total number of counts during n intervals, ∆tjirr and
∆tjcool the lengths of j-th irradiation interval and cor-
responding cooling time, respectively.
Reaction thresholds and used spectroscopic data of residual nuclei [27]
Reaction Residual Branching
Reaction threshold nucleus Half life Eg [keV] ratio
[MeV] [%]
96Ru(g, n) 10.693 95Ru 1.643 h 336.4 70.1 (5)
626.8 17.8(5)
98Ru(g, n) 10.189 97Ru 2.83 d 215.7 86 (5)
324.5 10.8(2)
100Mo(g, n) 8.289 99Mo 65.976 h 140.5 89(3)
181.1 5.99(7)
739.5 12.26(18)
777.9 4.3(8)
197Au(g, n) 8.071 196Au 6.1669 d 333.0 22.9(9)
355.7 87(3)
106
On the other hand (γ, n)-reaction yield is a con-
volution of the cross section σ(γ,n)(Eγ) with the
bremsstrahlung absolute spectrum Φγ(Eγ , E0) over
the photon energies:
Yact (E0) =
∫ E0
Sn
σγ,n (Eγ)Φγ (Eγ , E0) dEγ . (8)
As it was noticed in section 3.1 the reaction
197Au(γ, n)196Au was used as the standard one for
determination of the bremsstrahlung fluence. Apart
from earlier works the thorough researches of this
reaction have been revived after the year 2000 in
conjunction with the study of the γ-process stel-
lar nucleosynthesis. A number of scientific teams
have measured and analyzed its cross sections using
bremsstrahlung [22, 28, 29, 30] and laser Comp-
ton scattering γ-rays [31, 32, 33] paying attention
to the low energy region. Fig.9 illustrates the ex-
perimental values (points) of the 197Au(γ, n)196Au
reaction cross sections obtained in three recent
works [31, 32, 33] which are in accordance each
with other, and the fitted curve for the last data
set ranging to the near threshold energy region.
8 9 10 11 12 13
100
200
300
400
500
197Au( ,n)196Au
Hara 2007
Kitatani 2011
Itoh 2011
Fit
C
ro
ss
se
ct
io
n
[m
b]
Photon energy [MeV]
Fig.9. (Color online) Excitation function of the
197Au(γ, n)196Au reaction measured by different
teams. The points denote the experimental data of
Hara et al. [31], Kitatani et al. [32] and Itoh et al.
[33] the curve is polynomial fitting of Itoh et al.
data (red points)
The experimental integral yield values of the studied
and standard reactions derived from the activities of
the targets of the same irradiation together with ab-
solute cross sections of the 197Au(γ, n)196Au reaction
(the fitted curve in Fig.9) give possibility to draw the
rates of the studied reactions. In practice we used
the activation yield of the studied reaction reduced
to the gold reaction one, i.e.
Y red
act =
Yact(Target)
Yact(Au)
. (9)
4. THE EXPERIMENTAL RESULTS AND
COMPARISON WITH THE
THEORETICAL PREDICTIONS
We set ourselves as an object (i) to determine the ac-
tivation yields of the (γ, n)-reactions running on the
p-nuclei 96Ru and 98Ru in order (ii) to derive the re-
action rates at astrophysically interesting energy re-
gion and (iii) to compare them with the theoretical
predictions.
4.1. REACTION YIELDS
The experimental integral yields of the reac-
tions 96Ru(γ, n)95Ru, 98Ru(γ, n)97Ru as well as
100Mo(γ, n)99Mo as the test reaction calculated with
the activation equation are shown in Fig.10 as the
function of the bremsstrahlung end-point energy.
Fig.10. Experimental (points) and theoretical
(curves) integral yields of the (γ, n)-reactions on
96Ru, 98Ru and 100Mo reduced to the standard
197Au(γ, n)196Au reaction integral yields depending
on the bremsstrahlung end-point energy
The data are normalized to the standard
197Au(γ, n)196Au reaction yields. The dark points
represent our results while the light ones depict the
Tickner et al. data [34] for the two first reactions
and the Erhard et al. data [15] for the last one.
The agreement between results of ours and afore-
mentioned authors can be considered as satisfactory.
The solid curves in graphs represent the theoretical
values calculated in the frame of the H-F statistical
model incorporated by the NON-SMOKER code [9]
with the default input parameters providing a global
description for a wide range of isotopes: the neutron
optical potential of Jeukenne et al. [35] with a low-
energy modification of Lejeune [36], the radiation
strength function of Thielemann and Arnold [37] and
nuclear level density of the back-shifted Fermi-gas
model formalized by Rauscher et al. [38].
4.2. REACTION RATES
Fig.11 illustrates the experimental and theoretical
values of the reaction rates (vertical logarithmic axis)
107
in the most significant range of temperatures (hor-
izontal axis) for the γ-process stellar nucleosynthe-
sis located between T9 = 2 and T9 = 3.
10-10
10-6
10-2
102
2.0 2.5 3.0
10-9
10-5
10-1
103
96Ru( ,n)95Ru
Experiment
Theory
98Ru( ,n)97Ru
Experiment
TheoryR
ea
ct
io
n
ra
te
[
1/
s]
Temperature [GK]
2.0 2.5 3.0
0.4
0.8
Temperature [GK]
E
xp
/T
he
or
y
2.0 2.5 3.0
0.4
0.8
Temperature [GK]
E
xp
/T
he
or
y
2.0 2.5 3.0
Fig.11. Experimental (points) and theoreti-
cal (NON-SMOKER code) reaction rates of the
96Ru(γ, n)95Ru (upper panel) and 98Ru(γ, n)97Ru
(lower panel) reactions on dependence of star en-
vironment temperatures inherent to the γ − process
nucleosynthesis. Inserts are the ratios (linear ordi-
nate) of experimental values calculated using Wigner
approximation for the cross section energy depen-
dence (dark points) and superposition technique
(light points) to the theory predictions
The upper and lower graphs show the results for
the 96Ru(γ, n)95Ru and 98Ru(γ, n)97Ru reactions,
respectively. The points depict the reaction rates cal-
culated from the measured activation integral yields
while the curves from the theoretical values of the
cross sections predicted by the H-F statistical model
code NON-SMOKER [9]. As seen in the main plots
of Fig.11 the agreement of the experimental and the-
oretical reaction rates of each reaction is fairly well in
general despite the large difference between the abso-
lute values for the two studied reactions that is caused
by the different threshold energies (see Table). More
detailed visualization is presented in the inserts of the
panels where the ratios of the experimental reaction
rate values calculated with the Wigner approxima-
tion (dark points) and superposition technique (light
points) to the theoretical predictions are shown. Both
approximations give the similar results but the theo-
retical predictions overestimate the reaction rates by
(40...60)% in the considered temperature range.
5. CONCLUSIONS
The activation technique using the bremsstrahlung
of the NSC KIPT LINAC and gamma-ray spectrom-
etry was put to the test for the measurements of the
integral yields of the reactions 96Ru(γ, n)95Ru and
98Ru(γ, n)97Ru in order to determine the reaction
rates in the astrophysically interesting energy re-
gion just above the neutron emission threshold. The
default option of the NON-SMOKER code of the
statistical theory of nuclear reactions overestimates
the experimental reaction rates within a factor of
about 2. Similar measurements at NSC KIPT can be
extended in the nuclear mass number region A ∼ 100
containing a number of p-nuclei to supplement the
network of astrophysical photonuclear reactions for
the γ-process stellar nucleosynthesis simulation and
to test the statistical model parametrization.
ACKNOWLEDGEMENTS
The authors express their gratitude to Dr. S. Gokov
and the LINAC staff for providing target irradiation
procedure.
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ÀÊÒÈÂÀÖÈÎÍÍÀß ÌÅÒÎÄÈÊÀ ÈÇÌÅÐÅÍÈß ÑÊÎÐÎÑÒÅÉ
ÀÑÒÐÎÔÈÇÈ×ÅÑÊÈÕ ÔÎÒÎßÄÅÐÍÛÕ ÐÅÀÊÖÈÉ ÍÀ ÏÓ×ÊÅ ÒÎÐÌÎÇÍÎÃÎ
ÈÇËÓ×ÅÍÈß
È.Ñåìèñàëîâ, Å.Ñêàêóí, Â.Êàñèëîâ, Â.Ïîïîâ
Àñòðîôèçè÷åñêîå ìîäåëèðîâàíèå ïðèðîäíîé ðàñïðîñòðàí¼ííîñòè òàê íàçûâàåìûõ p-èçîòîïîâ òðåáó-
åò ñâåäåíèé î ñêîðîñòÿõ íèçêîýíåðãåòè÷íûõ (ïðèïîðîãîâûõ) ôîòîÿäåðíûõ ðåàêöèé íà îãðîìíîì ÷èñëå
àòîìíûõ ÿäåð. Íà ïðèìåðå (γ, n)-ðåàêöèé, âûçûâàåìûõ ôîòîíàìè â ÿäðàõ p-èçîòîïîâ 96Ru è 98Ru, ïðî-
äåìîíñòðèðîâàíà âîçìîæíîñòü ïîëó÷åíèÿ ñîîòâåòñòâóþùåé ýêñïåðèìåíòàëüíîé èíôîðìàöèè íà ïó÷êå
òîðìîçíîãî èçëó÷åíèÿ õàðüêîâñêîãî ëèíåéíîãî óñêîðèòåëÿ ýëåêòðîíîâ ïóò¼ì èçìåðåíèÿ èíòåãðàëü-
íûõ âûõîäîâ ðåàêöèé. Ïîëó÷åííûå ðåçóëüòàòû ñðàâíèâàþòñÿ ñ ïðåäñêàçàíèÿìè ñòàòèñòè÷åñêîé òåîðèè
ÿäåðíûõ ðåàêöèé.
ÀÊÒÈÂÀÖIÉÍÀ ÌÅÒÎÄÈÊÀ ÂÈÌIÐÞÂÀÍÍß ØÂÈÄÊÎÑÒÅÉ ÀÑÒÐÎÔIÇÈ×ÍÈÕ
ÔÎÒÎßÄÅÐÍÈÕ ÐÅÀÊÖIÉ, ÍÀ ÏÓ×ÊÓ ÃÀËÜÌIÂÍÎÃÎ ÂÈÏÐÎÌIÍÞÂÀÍÍß
I.Ñåìiñàëîâ, �.Ñêàêóí, Â.Êàñiëîâ, Â.Ïîïîâ
Àñòðîôiçè÷íå ìîäåëþâàííÿ ïðèðîäíî¨ ðîçïîâñþäæåíîñòi òàê çâàíèõ p-içîòîïiâ ïîòðåáó¹ çíàíü øâèäêî-
ñòåé íèçüêîåíåðãåòè÷íèõ (ïðèïîðîãîâèõ) ôîòîÿäåðíèõ ðåàêöié íà âåëè÷åçíié êiëüêîñòi àòîìíèõ ÿäåð.
Íà ïðèêëàäi (γ, n)-ðåàêöié, ñïðè÷èíÿ¹ìèõ ãàëüìiâíèì âèïðîìiíþâàííÿì õàðêiâñüêîãî ëiíiéíîãî ïðè-
ñêîðþâà÷à åëåêòðîíiâ â ÿäðàõ p-içîòîïiâ 96Ru òà 98Ru, ïðîäåìîíñòðîâàíî ìîæëèâiñòü îòðèìàííÿ âiä-
ïîâiäíî¨ åêñïåðèìåíòàëüíî¨ iíôîðìàöi¨ øëÿõîì âèìiðþâàííÿ iíòåãðàëüíèõ âèõîäiâ ðåàêöié. Îòðèìàíi
ðåçóëüòàòè ïîðiâíþþòüñÿ ç ïåðåäáà÷åííÿìè ñòàòèñòè÷íî¨ òåîði¨ ÿäåðíèõ ðåàêöié.
110
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