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POLITECNICO DI TORINO Repository ISTITUZIONALE

Antiproton stopping power in hydrogen below 120 keV and the Barkas effect / A. ADAMO; AGNELLO M.; F. BALESTRA;

G. BELLI; G. BENDISCIOLI; A. BERTIN; P. BOCCACCIO; G. C. BONAZZOLA; T. BRESSANI; M. BRUSCHI; M. P.

BUSSA; L. BUSSO; D. CALVO; M. CAPPONI; M. CORRADINI; S. COSTA; S. DE CASTRO; D. D'ISEP; I. V.

FALOMKIN; L. FAVA; A. FELICIELLO; L. FERRERO; V. FILIPPINI; R. GARFAGNINI; U. GASTALDI; P. GIANOTTI; A.

GRASSO; C. GUARALDO; F. IAZZI; A. LANARO; E. LODI RIZZINI; M. LOMBARDI; M. P. MACCIOTTA; A. MAGGIORA;

S. MARCELLO; U. MARCONI; G. V. MARGAGLIOTTI; G. MARON; M. MASALA; A. MASONI; I. MASSA; B. MINETTI;

M. MORANDO; M. MORGANTI; D. PANZIERI; G. PAULI; M. PICCININI; R. PIRAGINO; M. POLI; G. B. PONTECORVO;

G. PUDDU; R. A. RICCI; A. ROTONDI; A. M. ROZHDESTVENSKY; P. SALVINI; L. SANTI; M. G. SAPOZHNIKOV; G.

SARTORI; N. SEMPRINI-CESARI; S. SERCI; F. TOSELLO; V. I. TRETYAK; L. VANNUCCI; G. VEDOVATO; L.

VENTURELLI; A. VITALE; A. ZENONI; A. ZOCCOLI; G. ZOSI. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - 47:5(1993), pp. 4517-4520. [10.1103/PhysRevA.47.4517]

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Antiproton stopping power in hydrogen below 120 keV and the Barkas effect

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12 November 2021

PHYSICAL REVIEW A VOLUME 47, NUMBER 5 MAY 1993

Antiproton stopping power in hydrogen below 120 keV and the Barkas effect A.

Adamo,

' _M.

_Agnello,

" _F.

_Balestra,

' _G.

_Belli,

" _G.

Bendiscioli,

'

_{A. Bertin,}

P. Boccaccio, G. C.

Bonazzola,

' _T.

_Bressani,

' _M.

_Bruschi,

_{M. P.}

_Bussa,

' _L.

_Busso,

' _D.

_Calvo,

'

M.

Capponi,

C.

Cicalo,

' _M.

_Corradini,

_S.

_Costa,

' _I.

_D'Antone,

_S.

_{De Castro,}

_F.

_D'Isep,

'

A.

Donzella,

I.

V.Falomkin,

" _L.

_Fava,

' _A.

Feliciello,

' _L.

_Ferrero,

'

_V.Filippini,

' _D.

_Galli,

R.

Garfagnini,

' _U.

_Gastaldi,

_P.

_Gianotti,

' _A.

_Grasso,

' _C.

_Guaraldo, ^'

_F.

_Iazzi,

_A.

_Lanaro, ^'

E.

Lodi Rizzini,

M.

Lombardi, V.Lucherini, ^'

A.

Maggiora,

' _S.

_Marcello,

'

U. Marconi,

G.

Maron, A.Masoni,

' _I.

_Massa,

_B.

_Minetti,

_M.

_Morando,

_{' P.}

_Montagna,

' _F.

_Nichitiu,

" _D.

_Panzieri,

'

G.

Pauli,

M.

Piccinini,

G.

Piragino,

' _M.

_Poli,^'

_{G. B.}

Pontecorvo,

" _G.

_Puddu,

' _{R. A. Ricci,}

'"

E.

Rossetto,

' _A.

_Rotondi,

' _{A. M.}

Rozhdestvensky,

" _P.

_Salvini,

' _L.

_Santi,

_{M. G.}

Sapozhnikov,

"

_{N. Semprini Cesari,}

S.

Serci,

' _P.

_Temnikov,

" _S.

_Tessaro,

" _F.

_Tosello,

'

_V.

_I.

_Tretyak,

'" _{G. L.}

_Usai,

' _L.

_Vannucci, g

G.

Vedovato,

L.

Venturelli,

M.

Villa, A.Vitale,

G.

Zavattini, A.Zenoni,

' _A.

_{Zoccoli, and}

G.

^Zosi'

(OBELIX

Collaboration)

Dipartimento di Scienze Fisiche, Universita di Cagliari, Cagliari, Italy and Istituto Nazionale diFisica Nucleare, Sezione di Cagliari, I-09100Cagliari, Italy

Politecnico di Torino, Torino, Italy

and Istituto Nazionale diFisica Nucleare, Sezione di Torino, I-10150Torino, Italy Istituto diFisica, Universita di Torino, Torino, Italy

and Istituto Nazionale diFisica Nucleare, Sezione di Torino, I-1'0125Torino, Italy Dipartimento di Elettronica per l'Automazione, Universita degli Studi diBrescia, and Istituto Nazionale diFisicaNucleare, Sezione di Torino, I-25133Brescia, Italy

Dipartimento di FisicaNucleare eTeorica, Universita diPavia, and Istituto Nazionale di FisicaNucleare, Sezione di Pavia, I-27100Pavia, Italy

Dipartimento diFisica, ^{Universita di}Bologna,

and Istituto Nazionale diFisica Nucleare, Sezione diBologna, I-40100Bologna, Italy

sLaboratori Nazionali diLegnaro dell'Istituto Nazionale di FisicaNucleare,

I

^{35020Legnaro (P-adoua), Italy}

"JointInstitute forNuclear Research, Dubna, SU^IOIOOOMoscow, R-ussia Laboratori diFrascati dell Istituto Nazionale di FisicaNucleare, I-00044Frascati, Italy

Dipartimento diFisica, Universita diPadova,

and Istituto Nazionale diFisica Nucleare, Sezione diPadova, I-35100Padova, Italy Istituto diFisica, Universita di Trieste,

and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34127Trieste, Italy Dipartimento diEnergetica, Universita di Firenze, Firenze, Italy

and Istituto Nazionale di FisicaNucleare, Sezione diBologna, I-40100Bologna, Italy Istituto diFisica, ^{Universita di Udine,}

and Istituto Nazionale diFisica Nucleare, Sezione di Trieste, I-33100Udine, Italy (Received 27 July 1992)

The simultaneous measurement ofthe spatial coordinates and times ofPs annihilating at rest in aH2 target at very low density p (p/po ^&

10,

po being the STPdensity) gives the possibility ofevaluating the behavior ofthe pstopping power in H2at low energies (below 120 keV). Itisdifferent from that ofpro- tons (the Barkas effect). Moreover, it isshown that a rise at low-energy values (

~

1keV) isneeded to agree with experimental data.

PACS number(s): 34.50.Bw

Following the original work

of

Bohr

[1]

^{the high-}

energy (projectile velocity

))

^{e /fi) behavior}

^of

^{the stop-}

ping power is very ^well described by the Bethe [2]^formu- la for a point charge penetrating through matter at non- relativistic speed; it is proportional to the projectile charge squared

(Zt ).

Focusing on protons and antipro- tons (p⁾as projectiles at low velocity (v

=e

hrt) the Born

series is generally assumed to fail and other methods

of

calculating the consequences

of

collision are required. At very low velocity (v

(e

/A) a proton loses energy not only in electronic collisions which lead to excitation and ionization; elastic scattering by the screened nuclei is also important.

For

protons, the electronic stopping power has a maximum around the typical electron velocity,

i. e.

_,

47 4517 Q~1993The American Physical Society

4518

BRIEF

REPORTS 47

=55

keV for H2. Around and below the maximum, mea- surements are not ^well reproduced by theoretical esti- mates. The electronic contribution

to

the total energy loss in hydrogen is commonly assumed (e.g., in published tabulations [3]) to decrease linearly with the proton ve- locity forenergies below 10keV; see also

Ref. [4].

For

antiprotons, even the qualitative behavior

of

the stopping power is only poorly evaluated [5—

9]. For

_p ^'s at very low velocities, the energy loss due to excitation and ionization is expected to be considerably enhanced due to the so-called adiabatic ionization processes (see Refs. _[5—

7]). For

close collisions the passage

of

ap ^inside the orbital radius

of

a target electron will reduce the efFective nuclear charge seen by the electron which will lead to a release

of

the electron. This fact was first point- ed out by Fermi and Teller

[10],

who specifically con- sidered the ground state

of

a system consisting

of

a nega- tive muon and a molecule. The molecular mechanism peculiar to the case

of

hydrogen has been worked out _by Wightman

[5]. For

antiprotons colliding with atomic hy- drogen, Kimura and Inokuti [6]used a molecular-orbital expansion method to show that

if

the antiproton comes within a distance

R„=0.

64ao (ao is the Bohr radius,

0.

053nm) from the proton, then the target is ionized (the same R was found by Fermi and Teller).

Furthermore, a difference in the stopping power for positive and negative particles (the Barkas effect)

[11]

^has

been known fora long time, but lack

of

suitable antiparti- cle beams has prohibited quantitative studies [12—23]

of

the effect until recent years [24

—26].

With the advent

of LEAR

(low-energy antiproton ring) at

CERN,

a high-quality beam

of

antiprotons at low en- ergies became available, permitting accurate measure- ments

of

the stopping power for antiprotons down to 200 keV [24

—

_{26]and their ionization}

[27

^—

29].

To

study pp annihilations at rest, the

OBELIX

colla- boration [30]has realized a very low-density hydrogen target, ^the ratio between the experimental density p and the STP density _po ranging from 10 to

10,

^{and a to-}

tal

of

some 10 annihilation events has been collected.

These data are

of

great interest forthe evaluation

of

thep stopping power particularly from the energy region just above the maximum down to some hundreds

of

eV.

The

LEAR

machine delivers

to

our experiment a monochromatic 105-MeV/c gr beam, which passes through some materials (a

Be

window closing the beam pipe, a thin scintillator detector

So,

^variable air, and My- lar sheets) before entering the ultrapure (less than 1 ppm

of

other gases) hydrogen target, 75 cm long and 30cm in diameter. To maximize the fraction

of

ps annihilating at rest in the target it is desirable that the largest number

of

ps enter the target volume with a narrow momentum bite

and the appropriate nominal momentum. In the best ar- rangement

=45% of

ps are stopped in the Mylar window at the entrance

of

the target and the remaining ones enter the target volume with a momentum spectrum ranging from

0

to

=43

MeV/c. We measure this value with an empty target (

(10

^mbar) by time

of

flight. More ^de- tails

of

the experimental technique are given in

Ref. [30].

We have used three H2 pressure values

(p, =8. 20+0.

05, p2

=4. 10+0.

05 p

=2. 10+0.

05 mbar)

to

which corre-

spond three different

E '"(p

)for the kinetic energy

of

ps stopping and annihilating in the _Hz gas just before the end

of

the target. More important, the energy spread (from the minimum zero energy at the entrance) produces a distribution

of

the stopping points

of

the ps ⁱⁿ the (z,

t)

plane.

Figure ¹ shows the distribution

of

the experimental mean annihilation times (

t,

^{)in the target as a function}

^of

the path length (along the z beam direction) for the three values

of

the pressure. Experimentally,

t

for each event is measured _by the time at which the charged particles produced in the annihilation hit the scintillator barrel surrounding the target, relative to the starting time _to given by the p ^{crossing the beam} scintillator counter.

The time resolution isbetter than 1 ns. The annihilation times distributions are convolutions between the times

of

moderation

(t)

until the ps capture and the cascade times

(t„,

⁾

^of

the protonium atoms. We plotted the distribu- tion

of t,

corresponding to abin in z

of

2 cm, the experi- mental spatial resolution being ¹ cm. We found that all the distributions obtained in this way, ^well populated sta- tistically, had a constant width and were fully consistent with Gaussian distributions (see Fig. 2). As discussed in Ref.

[30],

^this circumstance allowed us to determine the (P-p) atom cascade widths. Furthermore, it indicates that a continuous slowing down picture for the p ^stop- ping power,

S(E),

may well be adopted. The error on the experimental mean values

of t,

^{foreach bin inzis}negligi- ble.

The experimental information contained in Fig. ¹may well be related to

S of p.

^{In fact the} p total path length R isevaluated by integration

of S,

700—

rIi 600—

500—

400—

300—

200—

100—

0—

I s i i i I

»

^{i s I}

«»

^I

»»

^I

» «

^I

«

^{i g I i i}

»

^{I i i i i I}

0 10 20 30 40 50 60 70 80

Path length (cm)

FICx.1. Bidimensional distributions ofthe mean pp annihila- tion times

(t,

) in the target as a function ofthe annihilation coordinate z for 8.2 mbar, curve a, 4.2 mbar, curve b, and 2.1

mbar, curve cH2 pressure values compared with the results of our best-fitting function; seeFig.3.

47

BRIEF

REPORTS 4519

60

lf} ~p

Q XQ

20

;0

0ZCO 00

I

600 700

Time

(ns)

~Pl m ~^{~ ~}

800 900 1000

FICx.2. Atypical experimental annihilation time distribution for a 2-cm-wide bin for events ⁱⁿ the target at aH2 pressure of 2.¹mbar.

E

l

EO

I

C3

L

CL0

C 2

CL O (f)

E

dE

=f. ^-' „,

and, analogously, the mean moderation time tby

10 10

Energy (kev)

10 10

E

dE

t=t t

(2)

E;

being the variable kinetic energy

of

each

p

^{at the be-} ginning

of

the target.

Two parameters enter in the annihilation distributions in the target, apart ^from

S:

(i)the mean kinetic energy

of

ps captured by protons (Eca~) ^{and (ii) the mean} cascade

time

of

the (p-p) atom,

(t,

^{t), whic—h} is different at the three pressures; see

Ref. [30].

The experimental data are the

(R;, t;+t„,

^{) mean values for the three} situations;

0&E; ~E ^'"(p

) with

E '"(p3)(E '"(pz)&E

'"(p&).

We outline that, contrary towhat was done with different probes (e.g.,

p

^),

S

is detertnined, with our technique, by the simultaneous solution

of

both space and time relation- ships (1)and (2). This is possible only with ps, due to their specific feature

of

the annihilation and with a so- phisticated and complete apparatus like

OBELIX.

In particular, the use

of

(2)allows us

to

avoid ambiguities or corrections inevitable in measurements in which only the spatial coordinate relationship (1)is used, and then

S

is derived from the projected range and not from the total range. Moreover, even

if

we suppose that around

10% of

events (typically with the higher annihilations times in any 2-cm-wide bin) are characterized by a greater total path length and the proper positioning would be in the neighboring bin, our distributions in practice do not change.

By ^numerical integration and with

E„P ~10

eV (see,

e.

g.,

Ref. [31)),

^we have obtained the best fit to the data (solid line in

Fig.

1)by means

of

the well-known parame- trization [3]

S

^'

=S, ,

^'

^{+Sh; '„,}

^with

^S„„=aEP

^and

S„; ^h=(242. 6/E)ln(1+1. 2X10 /E+0. ^{1159E), E}

^being

measured in keV. The fit was performed for the data ^be- tween

0.

7 and 120keV and we obtained

y„=0.

^{57 (99de-}

grees

of

freedom). Other parametrization functions fur- nished bad values

of g, ^.

^So, our methodology makes it possible

to

argue quantitatively that the present result isa good approximation tothe real stopping power. Figure ³ shows a comparison

of

the best-fitting function (curve b)

FIG.

3. Comparison between the proton stopping power in Hz, curve afrom Ref. [3),^and the region (the dotted area) ofac- ceptable behaviors for the antiproton one. Curve bisour best- fitting function and curves cand dare examples oflimiting ac- ceptable behaviors. A fast rise below 0.7 keV, necessary to ^ex- plain the data but not used in the fit, is indicated by a dotted line.

with that for the proton (curve a ).

The best-fitting value for _S&, did not affect the behav- ior

of S

at high energies.

Its

relative importance is,

e.

g.,

1%

at 10 MeV.

Furthermore, an increase

of 5

below

0.

7 keV is neces- sary in order to explain the experimental data. This is clearly shown in

Fig. 4. It

appears that, even by assum-

1600—

1400

1200

1000

800

600

400

200

|0

20 30 40 50 60 70 80 Path length (cm)

FIG.

4. Comparison between experimental data at 2.1mbar hydrogen pressure and proton behavior after Andersen and Ziegler [3],^with

E„, ^~

^10eV,

t„, ⁼

200 ns, curve a&,and

t„, ⁼⁰

ns, curve a2.

4520

BRIEF

REPORTS

ing

t„, ^=0,

no agreement with the data can be obtained by using an extrapolation down to zero proportional to U,

as used for protons by Andersen and Ziegler

[3].

^This

conclusion is independent from the circumstance that in (1)we use R projected, that we measure, instead

of R.

In order to explain the experimental data without a fast rise

of S

^we would need areduction (and not an increase)

of

R by afactor

10.

The following remarks may bedrawn.

(i)Between 10 and 120 keV the mean p ^{stopping power} in H2 is systematically lower than that

of

proton. We re- call that Sdrensen [9]^evaluated p ^stopping power about half that

of

proton below the stopping maximum.

(ii) The maximum in the p ^{stopping power is}

=(60+13)% of

that for proton.

(iii) The _{p stopping} power crosses that

of

the proton below 10keV.

(iv) With such a p stopping-power behavior, the cas- cade times at the three pressures

p„p2,

and p3 turn out

to be

100+10, 135+15,

and

200+25

ns, ⁱⁿ good agree- ment with our previous conclusions

[30].

In conclusion, the Barkas effect forhydrogen shows up clearly. We answer positively also asto the existence

of

a maximum in the antiproton stopping power, as for pro- ton, a question that has been posed; see,

e.

g.,Refs. [9,

16].

Finally a fast rise

of

the stopping power below

0.

^7keV is observed, in agreement with the qualitative previsions [6,7] originally proposed by Fermi and Teller

[10],

and evaluated for hydrogen by Wightman

[5].

A rise

of

the stopping power near zero kinetic energy was highlighted in the

p

^{stopping cross} section evaluation _by Cohen

[32],

^{and indicated} also by the indirect measurement

of

the energy loss

of p

in helium by Kottmann

[33].

Many thanks are due to Professor

E.

Zavattini for use- ful discussions and suggestions, and to Professor

G.

Manuzio for valuable discussions during the preparation

of

this manuscript.

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