A growing body of mortality research on immigrants has shown that the longer they live in this country, the worse their rates of heart disease, high blood pressure and diabetes. And while their American-born children may have more money, they tend to live shorter lives than the parents.

The pattern goes against any notion that moving to America improves every aspect of life. It also demonstrates that at least in terms of health, worries about assimilation for the country’s 11 million illegal immigrants are mistaken. In fact, it is happening all too quickly.

“There’s something about life in the United States that is not conducive to good health across generations,” said Robert A. Hummer, a social demographer at the University of Texas at Austin.

For Hispanics, now the nation’s largest immigrant group, the foreign-born live about three years longer than their American-born counterparts, several studies have found.

Why does life in the United States — despite its sophisticated health care system and high per capita wages — lead to worse health? New research is showing that the immigrant advantage wears off with the adoption of American behaviors — smoking, drinking, high-calorie diets and sedentary lifestyles.