Abstract
Objectives. To assess relationships between changes in population levels, health care access, health care grievances, and mortality in California prisons.
Methods. We examined 30 California prisons using June 2013 to May 2023 data from California Correctional Health Care Services and the California Department of Justice. Associations between prison occupancy rates and care access, health care grievances, and mortality were estimated in linear or generalized linear models controlling for staff vacancies and the characteristics of incarcerated people. Because of the prevalence of COVID-19-specific dynamics in prisons in 2020–2021, baseline models included data up to December 2019; data from January 2022 through May 2023 were added as a robustness check.
Results. Reductions in prison occupancy rates were associated with increased access to care. Associations were more pronounced when postpandemic data were added. However, decreasing occupancy rates were not associated with declines in health care grievances or mortality.
Conclusions. Lowering prison occupancy rates could help ensure better access to care, but it is not a panacea for alleviating varied health-related problems and dangers inside carceral facilities. (Am J Public Health. 2025;115(6):936–944. https://doi.org/10.2105/AJPH.2025.308011)
In 2011, the Supreme Court issued its Brown v Plata ruling, maintaining that health care in California’s prisons was below constitutional standards. The problem could not be remedied, according to the court, without the alleviation of severe prison overcrowding. The decision upheld an earlier ruling that California must decrease the number of people in its prisons from then current levels—about twice the population the facilities were designed to hold—to no more than 137.5% of capacity.1 The state’s 2011 Public Safety Realignment Act enshrined court mandates into law.2
California’s case, although unique, signified a growing acceptance of the idea that “the number of people behind bars must be reduced.”3(p240),4 Overall, the US prison population decreased 25% between 2010 and 2021; however, the nation’s incarceration rate remains staggeringly high in comparison with that of the 1970s, as well as in comparison with other countries.5 In California, the prison population decreased by 26% between 2006 and 2018, from 173 000 to 128 000.6 As of 2021–2022, there were slightly under 100 000 people detained in California prisons.7
Studies of health care access inside prisons, including how it changes in relation to population declines, are lacking. The National Commission on Correctional Health Care maintains that “large gaps in correctional health care research have hampered policy decision making in all aspects of health care organization, provision, and financing for incarcerated populations,” in part because there is a dearth of “standardized reporting networks” and “some correctional administrators may be hesitant to share information about their facilities.”8
California’s publicly accessible and longitudinal health care data dashboard, created in part to satisfy litigation-related requirements, makes it possible to conduct health systems research on one of the largest prison systems in the country and draw conclusions with wide-ranging implications. Analyzing and interpreting data from the dashboard, which includes measure of patient access, utilization, and outcomes, offers a unique opportunity to assess connections between changes in prison populations and health care services.9
In addition to considering health care access, we used California Department of Justice data to assess how changes in prison population levels relate to mortality. We contextualize our findings with limited existing data and studies on connections between prison mortality and population levels.
METHODS
We collected California prison data from the Health Care Services Dashboard, made available by California Correctional Health Care Services. The dashboard, launched in 2013, publishes a wide range of measures on health service delivery and characteristics of staff and populations at the state and prison levels. We used monthly data from June 2013 to May 2023, covering 35 prisons that remained operational for the duration of the period. We excluded 4 institutions considered to be specialty treatment or rehabilitation centers housing atypical populations in terms of health characteristics (California Health Care Facility, California Medical Facility, California Rehabilitation Center, and Substance Abuse Treatment Facility and State Prison) and 1 institution with missing data on key variables such as occupancy rates (California City Correctional Facility). A total of 30 prisons were included in our final analyses.
As a complement to the dashboard data, we examined individual mortality data from the California Department of Justice (accessed in December 2023).10 We extracted information on deaths that occurred among those detained in the same 30 prisons examined via the dashboard data who were under the custody of the Department of Corrections and Rehabilitation Adult Operations and Adult Programs and the Division of Juvenile Justice. We derived the number of deaths per month and institution on the basis of reported dates of death.
Our earliest data observations were from 2013, 2 years after Brown v Plata and the passage of the Prison Realignment Act, which fostered a decline in California’s incarcerated population.1 Given that COVID-19 had wide-ranging and unique effects on carceral facilities in 2020 and 2021, we used only prepandemic data (January 2013–December 2019) in our baseline model and added postpandemic data (January 2022–May 2023) in a robustness check.11
We plotted trends in the monthly total incarcerated population of the 30 prisons and averaged monthly occupancy rate across prisons from June 2013 to May 2023. We exploited temporal and cross-prison variations in occupancy rates to estimate associations between prison populations and health-related measures.
Variables
Our primary variable of interest was prison occupancy rate, defined as the incarcerated population relative to the prison design capacity on the final day of a reporting month. To examine health-related effects, we assessed access to care, grievances, and deaths. We selected summary measures with the most available observations and minimal changes (in names or definitions) over the study period. We ultimately examined 5 outcomes: access to medical care, access to mental health care, access to dental care, health care grievances (i.e., complaints filed by incarcerated people related to health care) received per 1000 incarcerated people, and deaths per 10 000 incarcerated people (definitions of various measures are provided in the Appendix, available as a supplement to the online version of this article at https://www.ajph.org).
Our covariates included characteristics of incarcerated people and facilities. We considered the percentage of incarcerated people aged 50 years or older; the percentage characterized as high-risk priority 1, high-risk priority 2, medium risk, and low risk (see the Appendix for definitions of risk categories); and the percentage with disabilities. We also considered facility-level supply side factors, specifically vacancies in medical, mental, and dental service staff positions. Because vacancy rates were not reported until January 2017, including them in the regressions considerably reduced the number of observations. We therefore present regressions with and without vacancy rates.
Statistical Analysis
We estimated the association between occupancy rates and each of the health-related outcomes. For the 3 outcomes measured as proportions (medical care access, mental health care access, and dental care access), we estimated generalized linear models with binomial distributions and logit link functions. For the 2 outcomes measured as rates (health care grievances received per 1000 incarcerated people and deaths per 10 000 incarcerated people), we fit linear regression models. Negative binomial models were also attempted for the latter 2 outcomes in an earlier version of this study. Although the estimates were qualitatively similar, some regressions did not reach convergency. We therefore report the linear regression results.
We show regressions with characteristics of incarcerated people first and then add staff vacancy variables. All of the models included prison, year, and month fixed effects. Standard errors were clustered at the prison level. All of our analyses were conducted with Stata version 18 (StataCorp LP, College Station, TX).
Our baseline analyses included observations from June 2013 to December 2019 (before the pandemic). As a robustness check, we repeated the analyses with additional observations from postpandemic periods (January 2022 to May 2023). We excluded data from 2020 and 2021, when prisons were most heavily affected by the COVID-19 pandemic.
RESULTS
Figure 1 shows monthly total populations and monthly average occupancy rates among 30 California prisons from June 2013 to May 2023 (prison-level trends are presented in Appendix Figure A, available as a supplement to the online version of this article at https://www.ajph.org). Prison populations and mean occupancy rates declined between 2013 and 2015 subsequent to the Prison Realignment Act. They then showed some uptick and fluctuations in the following years, with the mean occupancy rate mostly below 1.375 (or 137.5%), the limit set by the act. The prepandemic trend confirms existing studies regarding changes in California’s prison population after legal mandates to reduce the number of people incarcerated in state facilities.12,13 A deep plummet occurred after the onset of the pandemic in early 2020 as a result of the state’s attempt to manage the spread of the virus by reducing occupancy.14 In 2021, prison populations and occupancy rates started to rise, followed by small fluctuations, but remained at comparatively low levels.
FIGURE 1—
Monthly Total Populations and Mean Occupancy Rates of 30 California Prisons: June 2013–May 2023
We summarize the statistics of all of the variables used in our analyses in Table 1. Some variables had fewer observations because of missing values for certain months or institutions. Mental health care access measures were discontinued as of February 2020, and vacancy measures became available only as of January 2017. The 3 care access measures all had mean values close to or above 90%, suggesting that about 90% of medical, mental, or dental service requests were completed within the defined time frame. In a given month, there were about 30 health care grievances received per 1000 incarcerated people and about 2 deaths among every 10 000 incarcerated people. More than 20% of the individuals imprisoned were aged 50 years or older, about 6% were disabled, and about half were characterized as medium or high risk, which related to greater medical needs.
TABLE 1—
Care Access, Grievances, Deaths, and Prison Characteristics During the Prepandemic and Postpandemic periods: California, June 2013–May 2023
| Variable | June 2013–December 2019 | January 2022–May 2023 | ||
| No. | Mean (SD) | No. | Mean (SD) | |
| Outcome measures | ||||
| Medical care access, % | 2330 | 88 (10) | 487 | 88 (10) |
| Mental health care access, % | 2340 | 92 (8) | 0 | |
| Dental care access, % | 2322 | 94 (9) | 487 | 94 (7) |
| Grievances received, no. | 2340 | 29.94 (20.78) | 479 | 33.11 (29.43) |
| Deaths, no. | 2370 | 1.62 (2.62) | 486 | 2.24 (12.26) |
| Independent variables | ||||
| Occupancy, no. | 2370 | 1.38 (0.20) | 486 | 1.13 (0.23) |
| Incarcerated people aged 50 y or older, % | 2370 | 22 (12) | 486 | 26 (14) |
| Chronic disease burden | ||||
| High-risk priority 1, % | 2370 | 4 (5) | 486 | 6 (7) |
| High-risk priority 2, % | 2370 | 8 (8) | 486 | 10 (8) |
| Medium risk, % | 2370 | 38 (13) | 486 | 35 (12) |
| Low risk, % | 2370 | 51 (20) | 486 | 49 (22) |
| Disabled, % | 2370 | 6 (5) | 486 | 10 (8) |
| Staff vacancies | ||||
| Medical service staff, % | 1080 | 13 (5) | 487 | 20 (9) |
| Mental health service staff, % | 1080 | 19 (10) | 487 | 28 (12) |
| Dental service staff, % | 1080 | 5 (5) | 487 | 9 (8) |
Note. Observations vary by variable as a result of missing values. Mental health care access measures were discontinued as of February 2020. Vacancy variables were available only as of January 2017. High-risk priority 1, high-risk priority 2, medium risk, and low risk refer to the percentages of patients with different levels of chronic disease burdens; people characterized as high-risk priority 1 were those considered to be at the highest risk level, and people characterized as low risk were those considered to be at the lowest risk level. Grievances received and deaths were monthly counts per 1000 and 10 000 people, respectively. More detailed definitions are provided in the Appendix (available as a supplement to the online version of this article at https://www.ajph.org).
Staff shortages—especially among mental health professionals—are widely viewed as a major challenge in prisons, so we considered employee vacancy measures in our analysis.15 We found that, between January 2017 (when the measures became available) and December 2019, average vacancy rates were above 10% for medical service staff and close to 20% for mental service staff. The mean vacancy rate for dental service staff was the lowest, at about 5%. We added observations from January 2022 to May 2023 to the regressions in our robustness check analysis. Descriptive statistics for these observations are listed separately.
Tables 2 and 3 present estimates of occupancy rates from the generalized linear models for care access and the linear models for grievances and deaths. For ease of coefficient interpretation, we derived and report marginal effects from the generalized linear models. In the case of the linear models, the reported marginal effects were equivalent to the coefficient estimates. During the prepandemic period (June 2013 to December 2019), variations in occupancy rates showed negative associations with some of our health-related outcomes (Table 2). In the top panel of Table 2 (regressions with controls for characteristics of incarcerated people), 2 of the 3 access measures were significantly negative, indicating less access when the occupancy rate increased. When controls for staff vacancy were added to the regressions (bottom panel), there were still 2 access measures showing significant and negative estimates, although medical care became significant only in the bottom panel and dental care access became insignificant.
TABLE 2—
Estimated Associations Between Occupancy Rates, Care Access, Grievances, and Deaths With Prepandemic Data: California, June 2013–December 2019
| Medical Care Access, b (95% CI) or No. | Mental Health Care Access, b (95% CI) or No. | Dental Care Access, b (95% CI) or No. | Grievances Received, b (95% CI) or No. | Deaths, b (95% CI) or No. | |
| Regressions with controls only for characteristics of incarcerated people | |||||
| Occupancy | −0.03 (−0.09, 0.03) | −0.07 (−0.12, −0.01) | −0.06 (−0.12, −0.00) | 13.61 (3.10, 24.12) | −0.54 (−1.49, 0.42) |
| No. | 2330 | 2340 | 2322 | 2340 | 2370 |
| Regressions with controls for staff vacancies and characteristics of incarcerated people | |||||
| Occupancy | −0.11 (−0.21, −0.01) | −0.11 (−0.19, −0.02) | −0.05 (−0.11, 0.01) | 10.31 (−3.46, 24.07) | −0.47 (−2.67, 1.73) |
| No. | 1080 | 1080 | 1032 | 1050 | 1080 |
Note. CI = confidence interval. Reported are estimated marginal effects of occupancy rates from 5 regressions based on monthly observations from June 2013 to December 2019. The first 3 regressions are generalized linear models, and the other 2 are linear regressions. The regressions also include characteristics of incarcerated people (percentage who were aged 50 years or older; percentage who were high-risk priority 1, high-risk priority 2, or medium risk; and percentage who were disabled), staff vacancy measures (percentages of vacancies in medical service, mental service, and dental service staff), and prison, year, and month fixed effects. Standard errors were clustered at the prison level. Full regression results are presented in Appendix Table A (available as a supplement to the online version of this article at https://www.ajph.org).
TABLE 3—
Estimated Associations Between Occupancy Rates, Care Access, Grievances, and Deaths With Additional Postpandemic Data: California, June 2013–December 2019 and January 2022–May 2023
| Medical Care Access, b (95% CI) or No. | Mental Health Care Access, b (95% CI) or No. | Dental Care Access, b (95% CI) or No. | Grievances Received, b (95% CI) or No. | Deaths, b (95% CI) or No. | |
| Regressions with controls only for characteristics of incarcerated people | |||||
| Occupancy | −0.05 (−0.10, −0.01) | −0.07 (−0.12, −0.01) | −0.05 (−0.08, −0.01) | −7.90 (−30.11, 14.31) | −6.46 (−17.36, 4.44) |
| No. | 2816 | 2340 | 2808 | 2819 | 2856 |
| Regressions with controls for staff vacancies and characteristics of incarcerated people | |||||
| Occupancy | −0.11 (−0.16, −0.06) | −0.11 (−0.19, −0.02) | −0.04 (−0.07, −0.02) | −21.64 (−58.93, 15.66) | −11.68 (−32.21, 8.84) |
| No. | 1566 | 1080 | 1518 | 1529 | 1566 |
Note. CI = confidence interval. Reported are estimated marginal effects of occupancy rates from 5 regressions based on monthly observations from June 2013 to December 2019 and January 2022 to May 2023. The first 3 regressions are generalized linear models, and the other 2 are linear regressions. The regressions also include characteristics of incarcerated people (percentage who were aged 50 years or older; percentage who were high-risk priority 1, high-risk priority 2, or medium risk; and percentage who were disabled), staff vacancy measures (percentages of vacancies in medical service, mental service, and dental service staff), and prison, year, and month fixed effects. Mental health care access regressions are the same as in Table 2, because mental health care measures had no observations in the postpandemic periods. Standard errors were clustered at the prison level. Full regression results are presented in Appendix Table B (available as a supplement to the online version of this article at https://www.ajph.org).
For our mental health care access measure, estimates indicated that a 10-percentage-point increase in occupancy rate, for example, was associated with a 1.1-percentage-point decrease in the measure when staff vacancy measures were included (or 0.7-percentage-point decrease when vacancy measures were not included). The number of grievances increased in response to occupancy increases but became insignificant after control for staff vacancy rates. Notably, death rates exhibited no significant change as occupancy rates changed.
The inclusion of additional staff vacancy variables helped control for supply side factors that might influence health-related outcomes. However, because of the lack of observations before 2017, adding the vacancy variables also reduced the observations for the regressions by more than half. To compensate for the loss of observations, we conducted a robustness check by including postpandemic years, during which we had more observations for staff vacancies. The results (Table 3) confirmed the reduction in access as occupancy rates increased. All 3 access measures were significantly negative (the estimates for mental health care access remained the same in Tables 2 and 3 because access to mental health care was measured only until February 2020; there were no postpandemic observations). Again, no significant reduction was found in health care grievances or deaths relating to occupancy rate increases.
DISCUSSION
Our study reveals that prison occupancy rates relate to access to health care but not prison mortality or numbers of grievances filed. In the context of the limited literature on prison overcrowding, mortality, and grievances, these findings are not as paradoxical as they may first appear. They suggest that a decline in prison population levels could increase the likelihood that an incarcerated person is seen by a health care provider but have muted effects on satisfaction with health care services and chances of death.
Controlling for various factors, we found that in less full prisons, people were more likely to have access to medical, mental, and dental care. Although this is the first study to our knowledge that quantifies the relationship between prison-based access to care and changes in prison occupancy levels, our findings align with previous qualitative research demonstrating that people in overcrowded prisons in and beyond the United States face particular dangers. High prison occupancy rates, studies show, can lead to an increased risk of violence16 and “late or inadequate medical care.”17 Prison administrators report that “rising populations” make it “harder to manage prisons effectively” because of increased “pressure on resources”; overcrowding has “a wide-ranging impact on prisoner health and wellbeing.”18 Researchers further note that overcrowding can accentuate fears of communicable disease, increase “psychological and emotional burden,” and limit access to basic resources.19 Our study offers quantitative evidence that a decline in access to care is an added cost of overcrowding, one that can further exacerbate its other harms.
In contrast with results suggesting impediments in access to care, we found that higher prison occupancy rates do not relate to higher mortality. Our results correspond with national data suggesting that prison population levels and mortality are not correlated. Data from the Bureau of Justice Statistics reveal that, between 2009 and 2019, the population of people in state or federal prisons fell by 18.9%20 as the prison mortality rate increased from 259 per 100 000 to 330 per 100 000. Although the number of deaths from drug or alcohol intoxication increased during that period, almost 90% of deaths in prisons were from illnesses such as cancer and heart disease.21 These findings reflect that a variety of factors relate to deaths in custody, including the demographic characteristics of imprisoned people and widespread health disparities as well as facility characteristics such as turnover rates.22
Our findings help explain the results of a 2023 study of California’s prison mortality rates between 2011 and 2014 that revealed that crude mortality increased immediately after the implementation of legislation intended to decrease prison populations. The mortality increase had little to do with facility crowdedness, the authors maintained, but instead was related to demographics. During the 3 years of the study, California’s decreasing prison population became, on average, older. Age-adjusted mortality rates were lower and showed greater declines in comparison with both unadjusted rates in California and age-adjusted rates in other states. The reason for this declining mortality, according to the study authors, could be that “de-population of California prisons … occurred in tandem with dedicated and seemingly effective efforts to improve the quality of medical care provided to prisoners.”13(p14)
Building on this work, in our assessment of relationships between prison population levels and health-related outcomes, we tracked change over a relatively extended period (2013–2023) in 30 prisons and controlled for incarcerated people’s age, medical risk, and disability as well as facility characteristics such as staffing levels.
Our finding that mortality is unrelated to prison occupancy rates underscores that, although lowering prison populations is a positive step forward, it does not alleviate many of the dangers faced by incarcerated people. As noted by Rowe et al., the Supreme Court opinion in Brown v Plata stipulated that overcrowding was “the primary reason for healthcare deficiencies,” but it also “made clear that resolving overcrowding alone would not be sufficient to improve the quality of care for prisoners.”13(p14) Incarcerated people are disproportionately likely to have a variety of health problems and, for many, according to a study of immigrant detention centers, “health harms of detention could be mitigated through release.”23(p733),24
Likewise, our results pertaining to grievances reflect that access to care is but 1 health-related challenge faced by incarcerated people. In one of the few studies assessing the nature and fate of incarcerated people’s grievances, Calavita and Jenness note that health-related complaints were by far the most common type of complaint filed in California prisons in the 2000s, accounting for 20% of the 16 kinds of grievances reviewed. Health-oriented grievances, the authors maintained, were related not only to accessing care but also to “contesting the quality of the care” received.25(p38) This helps explain why we found that, despite decreasing occupancy and increasing access, rates of grievances remained relatively stable.
In short, decreasing prison occupancy while maintaining staffing levels may improve people’s chances of seeing a health professional, but it is not a panacea. It does not change the fact that incarcerated people are generally less healthy than their counterparts in the free world and that prison health systems are riddled with challenges related to, for example, lack of oversight, low staff morale, and profiteering.26,27 Policies that focus on decreasing the number of people inside prisons should be viewed as potentially effective means of ensuring both that fewer people will experience the many dangers of incarceration and that those who are incarcerated have better access to care. But they are not “magic bullets” that solve all problems related to prison health services and outcomes.
Limitations
Health Care Services Dashboard data were not available until 2013, after the 2011 passage of the Public Safety Realignment Act, making prestudy– poststudy comparisons infeasible. However, we leveraged gradual changes in prison populations after the ruling and examined their association with health care access and outcomes.
Although Health Care Services Dashboard data include a variety of health service measures, they do not contain information on all characteristics of incarcerated people, staff, and prisons. We used panel data to control for time-invariant unobservable variables. With prison, year, and month fixed effects, we controlled for prison-specific and period-specific effects. We considered individuals’ age and health status; future studies might explore the possibility of examining additional characteristics.
Although California Department of Justice mortality data are reviewed by the California Criminal Justice Statistics Center with respect to validity, consistency, and completion, the veracity of death statistics from jails and prisons nationwide has been questioned.10,28
Our analyses did not reveal statistically significant effects of occupancy rates on mortality rates. Given that deaths are relatively rare events and that occupancy rates vary only within certain levels, such effects may be difficult to detect within our data sets.
The employee vacancy measure we used accounted for positions held or left vacant by civil service staff members. Sources suggest that the California Department of Corrections and Rehabilitation relied on external contractors to provide some medical services in this period, but the extent and exact nature of medical outsourcing are unclear; an audit ordered by the state’s legislature in May 2024 is pending.29
Finally, our evidence is drawn from a single state, and the generalizability of our findings may thus be limited. However, the changes studied here offer insights into the results of a directed and sweeping effort to reduce prison populations. Experiences in California provide valuable insight into ongoing discussions related to decarceration.
Conclusions and Policy Implications
Our study provides a powerful justification for pursuing decarceration: it can improve access to medical care for imprisoned people. Alongside research demonstrating that lowering incarceration rates does not generate increases in crime30,31 and that imprisonment (especially in overcrowded facilities) poses various dangers, this should serve as a call to action for policymakers and advocates concerned with improving prison and community health.
Stakeholders must be wary of focusing on alleviating overcrowding rather than the broader goal of decreasing carceral populations. For decades, judges have ordered corrections officials to decrease overcrowding as a means of ensuring the health and safety of people inside prisons. But through the 1990s, litigation related to overcrowding, in fact, had no discernible impact on prison fullness.32 Corrections officials, politicians, and others used court decisions indicting inhumane and overcrowded conditions as grounds to argue for more funding and more facilities as harsh sentencing laws led to yet higher rates of incarceration. Indeed, at the turn of the 21st century, lawsuits intended to foster decarceration had a paradoxical and unintended consequence: they contributed to the growth of prison systems and populations.33
California appears to have avoided that fate; however, to fully assess the health-related implications of policies related to reducing the number of people in prisons, it is necessary to consider their effects on other types of carceral facilities. After Brown v Plata, a massive reduction in the prison population was achieved, in part, by detaining people in county jails who would otherwise have been sent to prisons.34 Notably, health-related conditions in jails are often dire.35 We found that access to care in California prisons improved as the number of imprisoned people decreased; further studies might examine health-related jail conditions in California in the same period. In the meantime, policymakers aiming to bolster public health should consider decarceration strategies that do not merely shuffle people from one punishment bureaucracy to another but instead enable them to remain in the community.23
Our findings related to mortality and grievances underscore that more research is needed on health care quality and outcomes inside prisons. After all, a variety of factors aside from prison occupancy rates influence incarcerated people’s health-related experiences. Some of those factors relate to shortfalls in public health and social welfare systems in the free world and others to conditions inside. Sending fewer people to prison, although a step in the right direction, is not a panacea for alleviating the varied health-related problems and dangers inside carceral facilities.
ACKNOWLEDGMENTS
Funding for this project was made possible by grant G13LM013522 from the National Library of Medicine of the National Institutes of Health.
We thank the reviewers and editors for critical and constructive feedback.
Note. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
CONFLICTS OF INTEREST
The authors have no conflicts of interest to declare.
HUMAN PARTICIPANT PROTECTION
Publicly accessible California prison data and mortality data were used in this study. The former data set provides aggregated information at the facility level, without individual-level information. The latter data set provides deidentified information from deceased individuals. In both cases, the data sets do not meet the regulatory definition of human participant research. Thus, no institutional review board approval was needed for this study.
See also Goldhaber-Fiebert, p. 819.
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