The Elizabeth Center for Cancer Detection in Los Angeles — one of the oldest cancer screening clinics in California — plans to shut down today after treating its last patients. The center is a victim of Gov. Arnold Schwarzenegger’s decision to freeze enrollment in a cancer screening program for low-income women on Jan. 1 and pay for routine mammograms only for women after the age of 50. Those moves caused an abrupt drop in the Elizabeth Center’s patient load and revenues, which had already been strained as its costs exceeded what it was earning from the state.