Quasielastic $(e,{e}^{\ensuremath{'}}p)$ reaction on $^{12}\mathrm{C},^{56}\mathrm{Fe}$, and $^{197}\mathrm{Au}$

Quasielastic $(e, e^{'} p)$ reaction on ${}^{12}C, {}^{56}{Fe}$ , and ${}^{197}{Au}$

D. Dutta et al.

Phys. Rev. C 68, 064603 – Published 9 December 2003

Abstract

We report the results from a systematic study of the quasielastic $(e, e^{'} p)$ reaction on ${}^{12}C, {}^{56}{Fe}$ , and ${}^{197}{Au}$ performed at Jefferson Lab. We have measured nuclear transparency and extracted spectral functions (corrected for radiation) over a $Q^{2}$ range of $0.64 - 3.25 {(GeV ∕ c)}^{2}$ for all three nuclei. In addition, we have extracted separated longitudinal and transverse spectral functions at $Q^{2}$ of 0.64 and $1.8 {(GeV ∕ c)}^{2}$ for these three nuclei (except for ${}^{197}{Au}$ at the higher $Q^{2}$ ). The spectral functions are compared to a number of theoretical calculations. The measured spectral functions differ in detail but not in overall shape from most of the theoretical models. In all three targets the measured spectral functions show considerable excess transverse strength at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ , which is much reduced at $1.8 {(GeV ∕ c)}^{2}$ .

13 More

Received 24 March 2003

DOI:https://doi.org/10.1103/PhysRevC.68.064603

Authors & Affiliations

Click to Expand

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 68, Iss. 6 — December 2003

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(Color online) Comparison of calculated (dark line) and measured (light line) distributions. Top row depicts momentum, angle, and out-of-plane angle for electrons and the middle row the same for protons. Last picture depicts the projection of the distribution along the target for electrons.Reuse & Permissions
Figure 2
(Color online) Measured missing energy spectra for hydrogen (dark line) compared to spectra calculated using the Monte Carlo code SIMC (light line). The top left and middle right panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ and the middle left and bottom left panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 1.80 {(GeV ∕ c)}^{2}$ . These are the $L − T$ separation kinematics.Reuse & Permissions
Figure 3
Measured missing energy spectra for carbon at the different $Q^{2}$ . The top left and middle right panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ and the middle left and bottom left panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 1.80 {(GeV ∕ c)}^{2}$ . These are the $L − T$ separation kinematics.Reuse & Permissions
Figure 4
Measured missing energy spectra for iron at the different $Q^{2}$ . The top left and middle right panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ and the middle left and bottom left panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 1.80 {(GeV ∕ c)}^{2}$ . These are the $L − T$ separation kinematics.Reuse & Permissions
Figure 5
Measured missing energy spectra for gold at the different $Q^{2}$ . The top left and middle right panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ and the middle left and bottom left panels refer to the forward and backward electron angle kinematics, respectively, at $Q^{2} = 1.80 {(GeV ∕ c)}^{2}$ . These are the $L − T$ separation kinematics.Reuse & Permissions
Figure 6
(Color online) Momentum distributions for carbon $p$ shell (top panel, $10 < E_{m} < 25 MeV$ ) and $s$ shell (bottom panel, $30 < E_{m} < 50 MeV$ ). They have been normalized so that the integral of the measured spectral functions over $∣ p_{m} ∣ < 300 MeV ∕ c$ is equal to the integral of the spectral function at $Q^{2}$ of $1.8 {(GeV ∕ c)}^{2}$ .Reuse & Permissions
Figure 7
(Color online) Momentum distributions for iron integrated over an $E_{m}$ range $0 < E_{m} < 80 MeV$ . They have been normalized so that the integral of the measured spectral functions over $∣ p_{m} ∣ < 300 MeV ∕ c$ is equal to the integral of the spectral function at $Q^{2}$ of $1.8 {(GeV ∕ c)}^{2}$ .Reuse & Permissions
Figure 8
Momentum distributions for gold integrated over an $E_{m}$ range $0 < E_{m} < 80 MeV$ . They have been normalized so that the integral of the measured spectral functions over $∣ p_{m} ∣ < 300 MeV ∕ c$ is equal to the integral of the spectral function at $Q^{2}$ of $1.8 {(GeV ∕ c)}^{2}$ .Reuse & Permissions
Figure 9
Measured missing energy spectral function for carbon at $Q^{2} = 1.28 {(GeV ∕ c)}^{2}$ compared to independent particle shell model (IPSM).Reuse & Permissions
Figure 10
(Color online) Measured momentum distribution for carbon at $Q^{2} = 1.28 {(GeV ∕ c)}^{2}$ in the $p$ -removal energy region (top panel, $10 < E_{m} < 25 MeV$ ) and $s$ -removal energy region (bottom shell, $30 < E_{m} < 50 MeV$ ) compared to theoretical predictions. The solid line is the IPSM; dashed line is IPSM with an $8 %$ $s$ -shell strength. Dotted line is a DWIA calculation from Zhalov et al. [36] and the dot-dashed line is the same DWIA calculation with color transparency included.Reuse & Permissions
Figure 11
Measured missing energy spectral function for iron at $Q^{2} = 1.28 {(GeV ∕ c)}^{2}$ compared to theoretical models. The solid line is drawn using the IPSM. The dashed line is a calculation from Benhar et al. [37] and the dot-dashed line is from calculations using the TIMORA code described in Ref. 38 with spreading widths taken from the IPSM.Reuse & Permissions
Figure 12
Measured missing energy spectral function for gold at $Q^{2} = 1.28 {(GeV ∕ c)}^{2}$ compared to the IPSM.Reuse & Permissions
Figure 13
(Color online) Measured momentum distribution for iron integrated over an $E_{m}$ range $0 < E_{m} < 80 MeV$ at $Q^{2} = 1.28 {(GeV ∕ c)}^{2}$ , compared to theoretical predictions. Solid line is drawn using the IPSM. Dotted line is DWIA calculation from Zhalov et al. [36] without including color transparency and dot-dashed line is the same with color transparency included. Dot-dot-dash line is a calculation from Benhar et al. [37] and dash-dot-dash line is from calculations using the TIMORA code described in Ref. 38.Reuse & Permissions
Figure 14
Measured momentum distribution for gold integrated over an $E_{m}$ range $0 < E_{m} < 80 MeV$ at $Q^{2} = 1.28 {(GeV ∕ c)}^{2}$ compared to theoretical predictions. Solid line is drawn using the IPSM model and dashed line is a calculation from Benhar et al. [37].Reuse & Permissions
Figure 15
Normalized transparency as a function of angle relative to the conjugate angle for carbon (top), iron (middle), and gold (bottom). Normalization was done at the conjugate angle. The solid circles and squares correspond to forward angle and backward angle kinematics, respectively, at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ .Reuse & Permissions
Figure 16
Transparencies as a function of $Q^{2}$ . The solid squares and triangles are from the present work and at both 0.64 and $1.8 {(GeV ∕ c)}^{2}$ one of the points is slightly offset so that the forward and backward angle (solid triangles) results can be shown separately. Also shown are results reported from experiments at Bates [1] (open square) and SLAC [2, 3] (open triangle) and the followup to this experiment [4] (solid stars) at JLab.Reuse & Permissions
Figure 17
Iron separated spectral functions integrated over a $p_{m}$ range $0 < p_{m} < 80 MeV ∕ c$ . The $Q^{2} = 1.8 {(GeV ∕ c)}^{2}$ points have been displaced slightly for clarity. The lowest $E_{m}$ point has been averaged over $10 < E_{m} < 25 MeV$ . In obtaining these spectral functions the proton electric form factor was assumed to have the dipole form and the proton magnetic from factor was taken from Ref. 7.Reuse & Permissions
Figure 18
Gold separated spectral functions integrated over a $p_{m}$ range $0 < p_{m} < 80 MeV ∕ c$ . In obtaining these spectral functions the proton electric form factor was assumed to have the dipole form and the proton magnetic from factor was taken from Ref. 7.Reuse & Permissions
Figure 19
Comparison of the carbon longitudinal (top panel) and transverse (bottom panel) spectral functions at $Q^{2} = 0.64 {(GeV ∕ c)}^{2}$ , integrated over a $p_{m}$ range $0 < p_{m} < 80 MeV ∕ c$ , using the proton form factors obtained by the Rosenbluth separation [9, 10] (open symbols) and the polarization transfer [11] methods (solid symbols). The lowest $E_{m}$ point has been averaged over $10 < E_{m} < 25 MeV$ .Reuse & Permissions
Figure 20
Comparison of the carbon longitudinal (top panel) and transverse (bottom panel) spectral functions at $Q^{2} = 1.8 {(GeV ∕ c)}^{2}$ , integrated over a $p_{m}$ range $0 < p_{m} < 80 MeV / c$ , using the proton form factors obtained by the Rosenbluth separation [9, 10] (open symbols) and the polarization transfer [11] methods (solid symbols). The lowest $E_{m}$ point has been averaged over $10 < E_{m} < 25 MeV$ . The polarization transfer form factor points have been displaced slightly for clarity.Reuse & Permissions

Physical Review C

covering nuclear physics

Quasielastic $(e, e^{'} p)$ reaction on ${}^{12}C, {}^{56}{Fe}$ , and ${}^{197}{Au}$

D. Dutta et al.

Phys. Rev. C 68, 064603 – Published 9 December 2003

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review C

covering nuclear physics

Quasielastic (e,e′p) reaction on C12,Fe56, and Au197

D. Dutta et al.

Phys. Rev. C 68, 064603 – Published 9 December 2003

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Quasielastic $(e, e^{'} p)$ reaction on ${}^{12}C, {}^{56}{Fe}$ , and ${}^{197}{Au}$